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Trigonometry (Bank of Test Questions) 1. An 18-foot ladder is leaning against the side of a building forming a right triangle. The angle formed by the ladder and the ground is 60°. Which is closest to the distance, in feet, of the bottom of the ladder from the base of the wall? A. 9 B. 10.4 C. 12.7 D. 15.6 2. A diagonal of a square mirror is 10 inches long. What is the length, in inches, of each side of the mirror? A. 5 inches B. C. 10 inches inches D. inches 3. Workers at a botanical garden constructed a flower planter in the shape of a pentagon. The dimensions of the planter are shown below. What is the perimeter of the flower planter? A. Trigonometry feet B. feet C. Page 1/91 feet D. feet 4. Malcolm fastened an 85-inch clothesline to two walls that are 84 inches apart on level ground, as shown below. He fastened one end of the clothesline 55 inches above the ground on one wall, pulled the line tight, and then fastened the other end higher on the second wall. How many inches above the ground is the clothesline fastened to the other wall? A. 13 inches B. 56 inches C. 65 inches D. 68 inches 5. A right triangle is shown below. Which statement is always true? A. B. C. D. Trigonometry Page 2/91 6. Triangle JKL is similar to triangle PQR. The sine of angle L is What is the sine of angle R? A. B. C. D. 7. If Arc BE in the coordinate system below is the arc of a circle with the center at the origin, what is the length of ? A. 2 B. 3 C. 4 Trigonometry Page 3/91 8. In triangle ABC with right angle C, the measure of angle A is 37 degrees, and the length of the hypotenuse is 10. What is the length of A. 6 B. 7.5 C. 7.9 D. 12.5 9. What is the length of in Triangle ABC? A. 3 units B. 6 units C. 9 units D. 12 units Trigonometry Page 4/91 11. Calvin wanted to determine the amount of change, in degrees, that occurred in the elevation of the sun between 5:45 p.m. and 6:45 p.m. on April 5th. He decided to measure the length, in feet, of the shadow cast on the ground by his 5'10" height at both times. His results are shown in the table below. Based on Calvin’s results, which statement best describes the changes that occurred in the elevation of the sun between the given times on April 5th? A. The elevation of the sun decreased by 10.4 degrees. B. The elevation of the sun decreased by 13.0 degrees. C. The elevation of the sun decreased by 25.9 degrees. D. The elevation of the sun decreased by 29.1 degrees. 12. If cos(45°) 0.7071, what is sin(45°)? A. B. C. D. Trigonometry Page 5/91 13. A right triangle is shown below. Which equation represents a trigonometric ratio for the triangle? A. B. C. D. (sec = reciprocal of cos) 14. A gate is shown in the diagram. A wire brace is extended diagonally across the gate as shown. What is the length of the wire, x? A. 7 ft B. 6 ft C. 5 ft D. 4 ft 15. An escalator in a department store rises 80 feet at a 32° angle. What is the distance, x, from the bottom of the escalator to the top of the escalator, to the nearest foot? A. 94 feet B. 113 feet C. 128 feet D. 151 feet 16. In right CDF, m D 90º and m C 29º. The length of the hypotenuse is 10 centimeters. Using the table below, what is the length of A. 2.9 cm Trigonometry to two significant digits? B. 4.8 cm C. 5.5 cm Page 6/91 D. 8.7 cm 17. Right triangle ABC is shown below with the dimensions given in inches (in.). What is AB to the nearest tenth of an inch? A. 7.8 B. 10.4 C. 11.9 D. 13.7 18. A rope tied from a tent pole to a stake in the ground forms a 55° angle with the ground. The pole is 3 feet from the stake as shown below. What is the length of the rope, to the nearest tenth of a foot? A. 1.7 feet B. 3.7 feet C. 4.3 feet D. 5.2 feet Trigonometry Page 7/91 19. The diagonal of a square microchip is 0.141422 centimeters. Which measure, in square centimeters, is closest to the area of the microchip? A. 0.01 B. 0.02 C. 0.1 D. 1 21. George is building a rectangular gate. The dimensions of the gate are 6 feet high and 4 feet wide. He wants to fasten a thin brace diagonally at the corners to keep the gate sturdy. Approximately, how long is the brace? A. 4.0 feet B. 4.5 feet C. 7.2 feet D. 10 feet 22. A computer screen has a width of 15 inches and a height of 11 inches. Approximately what is the length of the screen’s diagonal? A. 10.2 inches B. 13.0 inches C. 18.6 inches Trigonometry Page 8/91 23. A computer screen has a diagonal dimension of 19 inches and a width of 15 inches. Approximately what is the height of the screen? A. 4.0 inches B. 11.7 inches C. 16.0 inches D. 24.2 inches 24. In right and If what is the length of A. 9.7 B. 17.3 C. 37.3 D. 38.6 25. The diagram below shows with the dimensions given in millimeters (mm). What is the sin(R)? A. B. C. Trigonometry Page 9/91 26. Juan’s house has a rectangular doorway that is 8 feet high and 3 feet wide. Which measurement is closest to the length of the diagonal of the doorway? A. 3.3 B. 7.4 C. 8.5 D. 11.0 27. What is the length of in the figure below? A. 8 units B. 12 units C. 14.4 units D. 20.8 units Trigonometry Page 10/91 28. What is the approximate value of x, in inches, in the triangle below? A. 17.2 B. 21.0 C. 30.0 D. 42.8 29. Triangle ABC is shown. Which of these statements about Triangle ABC is true? A. The Pythagorean Theorem proves that is a right triangle. B. The converse of the Pythagorean Theorem proves that C. The Triangle Inequality Theorem proves that is not a right triangle. D. The converse of the Triangle Inequality Theorem proves that Trigonometry Page 11/91 is a right triangle. is not a right triangle. 30. If and relation between a and b? which equation best describes the A. B. C. D. 31. A highway entrance ramp rises 4 feet above a horizontal road over a distance of 16 feet, as shown below. Which equation can be used to determine the angle formed by the horizontal road and the entrance ramp? A. B. C. D. Trigonometry Page 12/91 32. Joe used the Pythagorean theorem to make sure the picture frame he made is a precise rectangle. If Joe’s picture frame is a precise rectangle, how long is each diagonal in the rectangle above? A. 14 inches B. 20 inches C. 28 inches D. 34 inches 33. In is a right angle. If and what is the length of A. 20 cos 49° B. 20 sin 49° C. 20 tan 49° D. Trigonometry Page 13/91 34. Two planes leave the airport at exactly the same time and travel at the same average speed. One plane travels due north and the other travels due east as shown on the grid. How far apart are the planes after they have each traveled 700 miles? A. miles B. 1,050 miles C. 1,400 miles D. miles 35. A window at the top of a building is in the shape of an isosceles right triangle as shown in the figure. Which expression represents h, the distance from the peak of the window to its base in feet? A. B. C. 3 Trigonometry Page 14/91 36. The figure below shows If is an isosceles triangle, what is the approximate length of A. 23 B. 32 C. 39 D. 46 37. Helen constructed the spiral design shown below using seven right triangles. Both legs of the smallest triangle are 1 unit in length. The shorter leg of each of the remaining 6 triangles is 1 unit in length. What is x, the unit length of the hypotenuse of the largest triangle Helen used in the design? A. B. C. Trigonometry Page 15/91 38. Which equation shows a correct relation for triangle RSQ? A. B. C. D. 39. The figure below shows right triangle ABC and isosceles triangle ADC. Line segment BD is a straight line. Which of the following statements are true? I. II. III. A. I only B. I and III only C. II and III only Trigonometry Page 16/91 40. A triangle has sides of lengths 26 cm and 80 cm. The angle between these two given sides has a measure of 30°. What is the area of this triangle in square centimeters? A. 186 B. 520 C. D. 1040 41. Right triangle ABC is shown below with the dimensions given in units. What is the ? A. B. C. D. Trigonometry Page 17/91 42. The figure below shows right triangle where Which equation is true? A. B. C. D. 43. Right triangle ABC is shown below with the dimensions given in units. Which measurement is closest to BC in units? A. 3.9 B. 4.4 C. 4.6 Trigonometry Page 18/91 44. A 12-foot-tall pole is tethered to the ground by a wire at point T. Which expression could be used to determine the measure of the angle that the wire makes with the ground? A. B. C. D. 45. A ladder leaning against a wall makes an angle of 55° with the ground. If the foot of the ladder is 6.5 feet from the wall, what is the length of the ladder to the nearest hundredth? A. 3.73 ft B. 7.94 ft C. 9.28 ft D. 11.33 ft Trigonometry Page 19/91 47. Look at the isosceles right triangle below. What is the length of A. cm B. cm C. cm D. cm 48. Which of the following equations could be used to find the value of x in the right triangle below? A. B. C. Trigonometry Page 20/91 49. In the figure below, triangle ABC is similar to DEF. What is the value of Write your answer in simplified radical form. 50. Right triangle PQR is shown below with the dimensions given in units. Which ratio has a value equal to ? A. B. C. D. Trigonometry Page 21/91 51. Pentagon MNPQR is shown below. What is the length of A. B. C. D. 52. In a right triangle, if cos then what is sin x? A. B. C. Trigonometry Page 22/91 53. Benjamin is putting a fence around a right triangular garden. He has already used 12 ft of fencing for one side of the garden, which makes an angle of 65° with the longest side of the garden. To the nearest hundredth, how many feet of fencing will Benjamin need for the longest side? A. 28.39 B. 13.24 C. 10.88 D. 5.07 54. Triangle JKL is shown below. Which ratio represents A. B. C. D. Trigonometry Page 23/91 55. When Donelle stands at point R, he is 1000 feet from point S at the base of a cliff. When he looks up at an angle of 20°, he sees a friend at the top of the mountain cliff at point T. Which measurement is the closest to the height of the mountain cliff in feet? A. 342 B. 364 C. 940 D. 2747 56. The wind has blown a tree so that it is growing at a 108° angle with the ground. The top of the tree is 75 ft. from the ground. How tall is the tree? A. 71.3 ft. B. 75 ft. C. 78.9 ft. D. 93 ft. Trigonometry Page 24/91 57. A wire is attached 35 feet above the ground to a telephone pole. The wire makes an angle of 45° with the ground, as shown below. What is the length of the wire? A. B. feet C. feet D. 58. feet feet The current route used to travel by a vehicle between City A and City C through City B is shown on the coordinate grid below. A new road is under construction that will provide a direct route between City A and City C. If each grid unit represents 3 kilometers, which is closest to the difference in distance between the new route and the old route from City A to City C? A. 9.1 kilometers B. 12.1 kilometers C. 14.9 kilometers D. 19.1 kilometers Trigonometry Page 25/91 59. The entrance to the tent forms an isosceles right triangle as shown, and the support pole, modeled by forms an altitude to the hypotenuse. If how tall is the pole, in feet? A. 5 B. 6 C. 8 D. 10 60. In a right triangle, if tan then what is cos A. B. C. D. 61. Squares ACFG, BCDE, and ABJH have areas 144, 256, and 400 square units, respectively. Trigonometry Page 26/91 What are the dimensions of triangle ABC? A. B. C. D. 62. Jeff walked 54 meters along a river bank and saw a dock directly opposite him on the other side of the river. The river is 24 meters wide at the point where he saw the dock, as shown in the diagram below. Trigonometry Page 27/91 Which measurement is closest to the distance, in meters, of Jeff’s starting point from the dock? A. 30.0 B. 48.4 C. 59.1 D. 78.0 63. What is the length of the diagonal of a square if its side length is A. 7 inches B. 14 inches C. D. Trigonometry Page 28/91 inches? 64. If what is the value of x? A. B. C. D. 65. The length of the sides of a triangle are 5, 12, and 13 inches. Which statement is true about this triangle? A. The area of this triangle is 60 B. It is an acute triangle C. It is a right triangle D. The perimeter of this triangle is 25 in. 66. A 90-foot escalator rises a vertical distance of 45 feet, as shown in the diagram below. Trigonometry Page 29/91 What is the measure of the angle identified with a question mark in the diagram? A. 30° B. 45° C. 60° D. 90° 67. A guide wire for a palm tree makes a 32° angle with the ground and is staked 6 feet from the base of the tree, as shown below. What is the length, to the nearest tenth of a foot, of the guide wire from the ground to the palm tree? A. 7.1 feet Trigonometry Page 30/91 B. 8.5 feet C. 9.6 feet D. 11.3 feet 68. Julian is flying a kite attached to a 100-foot-long string. If the string is tied to the ground at an angle of elevation of 40°, what is the approximate height of the kite from the ground? A. 64 feet B. 77 feet C. 84 feet D. 100 feet 69. A 12-foot metal pole is leaning against a house, as shown below. The pole forms a 50° angle with the ground. How many feet, to the nearest tenth of a foot, is the base of the pole from the house? A. 6.0 feet Trigonometry Page 31/91 B. 7.7 feet C. 8.5 feet D. 9.2 feet 70. In a right triangle, if tan then what is cos x? A. B. C. 1 D. 71. In a right triangle, which of the following is the definition of the cosine ratio? A. B. C. D. 72. The dimensions of the right triangle shown below are given in units. Trigonometry Page 32/91 Which measurement is the closest to A. 20.6° B. 22.0° C. 68.0° D. 69.4° 73. An equilateral triangle ABC is shown in the figure below. If the height of is 30 centimeters, what is the length of a side of this triangle in centimeters? A. B. 15 C. 30 D. Trigonometry Page 33/91 74. For which value of is the statement true? A. 40° B. 50° C. 60° D. 140° 75. The diagonal of a square microchip is the area of the microchip? centimeters. Which measure, in square centimeters, is closest to A. B. C. D. 76. A sphere is cut by parallel Planes P and Q as shown below. Plane P passes through the center of the sphere, and Plane Q is located a distance of the radius of the sphere above the center. Trigonometry Page 34/91 What is the ratio of the area of the circular cross section formed by Plane P to the area of the cross section formed by Plane Q? A. 2 : 1 B. C. 4 : 1 D. 4 : 3 77. A ladder leaning against a wall makes a 55-degree angle with the floor. If the top of the ladder is 8 feet from the floor, which expression represents the length of the ladder in feet? A. 8(sin 45°) B. 8(cos 45°) C. D. 78. Tess is installing a support wire to the top of the tree in her yard. The angle the wire makes with a point on the ground 10 feet from the base of the tree is 75 degrees. How tall is the tree? Trigonometry Page 35/91 A. 13 feet B. 27 feet C. 37 feet D. 65 feet 79. A right triangle is shown below with the dimensions given in units. What is the value of x in units? A. 6 B. C. D. 12 80. If the base of a ladder is 5 feet from a building, how long must the ladder be to reach a window in the building that is 15 feet above the ground? A. 10.0 feet Trigonometry Page 36/91 B. 14.1 feet C. 15.8 feet D. 20.0 feet 81. In Which ratio represents the tangent A. B. C. D. 84. A person stands 10 feet away from the base of a 300-foot office building. Which equation could be used to find the angle of elevation? A. B. Trigonometry Page 37/91 C. D. 85. Right triangle ABC is shown. What is the length of A. B. C. D. 86. Sue made a quilt pattern from 16 congruent pieces of cloth shaped like isosceles right triangles. She cut the pieces so that the legs of each triangular piece are 6 inches long. Trigonometry Page 38/91 Which measurement is closest to x, the length in inches, of the hypotenuse of each triangular piece of cloth? A. 3.5 B. 4.2 C. 8.5 D. 18.0 87. A streetlight stands perpendicular to the ground. Martin measured the shadow of the streetlight. The distance between the base of the streetlight and the tip of the shadow is 15 feet. In terms of this situation, what could the expression below represent? A. the angle of elevation from the tip of the shadow to the top of the streetlight if the streetlight is 10 feet tall B. the height of the streetlight if the angle of elevation from the tip of the shadow to the top of the streetlight is 10 degrees C. the angle of elevation from the tip of the shadow to the top of the streetlight if the distance between Trigonometry Page 39/91 the tip of the shadow and the top of the streetlight is 10 feet D. the distance between the tip of the shadow and the top of the streetlight if the angle of elevation from the tip of the shadow to the top of the streetlight is 10 degrees 88. Josh was skiing down a slope where the angle of elevation was 14º. If the length of the slope was 1500 feet, what was the vertical drop of the slope? A. 374.0 feet B. 362.9 feet C. 1455.4 feet D. 6200.3 feet 89. In a right triangle, if , what is sin x? A. B. C. D. Trigonometry Page 40/91 90. A rope is tied from the top of a flagpole to a stake on the ground, as shown below. Which equation can be used to determine the value of x? A. B. C. D. Trigonometry Page 41/91 91. Which pair of trigonometric functions has the same value? A. B. C. D. 92. Spring Elementary School is having a door decorating contest. Mr. Xolo’s students want to use decorative tape to put an X on their door. The X will be so big that it touches each corner of the door. The door is 84 inches tall by 35 inches wide. Trigonometry Page 42/91 What is the amount of decorative tape, in inches, that the students will need to make the X? A. 91 inches B. 119 inches C. 182 inches D. 238 inches 93. Which of the following are lengths of the sides of a 30°–60°–90° triangle? A. B. 3, 4, and 5 units Trigonometry Page 43/91 C. D. 94. The diagram below shows and Part A. Find and compare Part B. Explain whether and and in these triangles. are similar. Use words, numbers, and/or pictures to show your work. 95. and Which expression represents the length of the altitude from Vertex A? A. B. Trigonometry Page 44/91 C. D. 96. A rectangular cake is 24 centimeters long, 11 centimeters wide, and 7 centimeters tall. The cake is cut perpendicular to and diagonally across the bases, as shown below. What is the perimeter, to the nearest centimeter, of the cross section formed by the cut? A. 64 centimeters B. 67 centimeters C. 70 centimeters D. 84 centimeters 97. Right triangle RST is shown below with the dimensions given in feet (ft). Which is closest to the measure of ? A. 15.1° Trigonometry Page 45/91 B. 15.7° C. 74.3° D. 74.9° 98. In is a right angle, and Which expression represents the length of ? A. B. C. D. 99. John is walking home with his younger brother, Don. Their home is on the opposite corner of a rectangular lot with dimensions of 500 feet by 800 feet. John decides to walk along two sides of the lot, while Don takes the direct diagonal path home. About how much farther does John walk than Don? A. 143 feet Trigonometry Page 46/91 B. 300 feet C. 357 feet D. 943 feet 100. A roof support is built according to the diagram shown below. What is the height of the roof in yards? A. 18 B. C. D. 36 101. Right triangle DEF is shown below. Trigonometry Page 47/91 What is DF to the nearest tenth of a meter? A. 10.7 B. 11.6 C. 25.1 D. 29.7 102. Right triangle RST is shown below with the dimensions given in feet (ft). Which is closest to RT? A. 6.4 Trigonometry Page 48/91 B. 7.1 C. 12.5 D. 15.7 103. Kristen created a space in her yard for a garden. She had three landscape timbers, each 8 feet in length. She positioned them in the form of a triangle, as shown in the drawing below. She drove a stake in the ground at Point C and another stake halfway between Points A and B, at Point D. She then ran a string between the two stakes to divide the planting area in half so she could plant half the garden with flowers and the other half with tomatoes. • What is the measure of • What is the length of Show all work or explain your answer. and the length of Show all work or explain your answer. • What is the total area of Kristen’s garden? Show all work or explain your answer. 104. The diagonal of a small square tabletop is 30 inches long. What is the length of each side of the tabletop in inches? A. 15 B. Trigonometry Page 49/91 C. D. 105. Which of the following equations can be used to verify the identity A. B. C. D. 106. In feet, and feet. What is the approximate area of feet? A. 43 B. 541 C. 625 D. 1083 Trigonometry Page 50/91 in square 107. A right triangle with dimensions given in units is shown below. What is the value of x in units? A. B. C. D. 108. A manufacturer is designing a square computer chip with a gold filament along its perimeter. If the diagonal of the chip is surround the chip? Trigonometry millimeters (mm), what is the length of the gold filament that will Page 51/91 A. B. C. 9 mm D. 24 mm 109. In Which ratio represents the cosine of Angle Q? A. B. C. D. 110. Brandon sights a helicopter above a building that is 200 feet away at an angle of elevation of 30º. To the nearest foot, how high above the ground is the helicopter? A. 100 B. 115 C. 170 D. 173 Trigonometry Page 52/91 111. The dimensions of shown below are in units. Which ratio represents the value of A. B. C. D. 112. Which of the following equations could be used to find the value of x in the right triangle below? A. Trigonometry Page 53/91 B. C. D. 113. A 13-foot ladder is resting against a building 12 feet above the ground. What is the angle formed by the ladder and the ground? A. 23° B. 43° C. 47° D. 67° 114. From a watch site on a ship, the angle of depression to a raft is 10 degrees. The site is 94 feet above sea level. Trigonometry Page 54/91 How far is the raft from the ship? A. 94 feet B. 92 feet C. 123 feet D. 533 feet 115. In and the length of the hypotenuse is 10 units. Using the information below, what is the length of A. 2.9 units B. 4.8 units C. 5.5 units D. 8.7 units 116. The figure below shows a right triangle and a rectangle. Trigonometry Page 55/91 What is the area of the figure? Round your answer to the nearest whole number. A. 72 in. B. 60 in. C. 55 in. D. 42 in. 117. Part of a two-column proof is shown. Trigonometry Page 56/91 Which conclusion can be derived from this proof? A. The sine and the cosine of vertical angles are equal. B. The sine and the cosine of congruent angles are equal. C. The sine and the cosine of supplementary angles are equal. D. The sine and the cosine of complementary angles are equal. Trigonometry Page 57/91 118. The isosceles right triangle below has an area of 98 square feet. What is the length of the hypotenuse in feet? A. 14 B. 19.8 C. 24.2 D. 28 119. In the figure below, what is the sin ? A. B. C. Trigonometry Page 58/91 D. 120. Tom is feet tall. If Tom stands 30 feet from the base of an apple tree looking up at an apple in the tree at an angle of sight of 48°, how far is the apple from the ground? A. 25.6 feet B. 27.8 feet C. 33.2 feet D. 38.8 feet 121. A right triangle is shown below. Trigonometry Page 59/91 Which expression represents the value of A. B. C. D. 122. Diagonal divides rectangle PQRS into two congruent triangles as shown below. What is the length of in feet? A. B. Trigonometry Page 60/91 C. D. 123. Roy drove his boat from a dock due north for 6 miles. He then turned and drove the boat due west for about 8 miles and dropped anchor. Approximately how many miles from the dock did Roy drop anchor? A. 2 B. 5.3 C. 10 D. 14 124. The top of an 18-foot ladder touches the side of a building 14 feet above the ground. Approximately how far from the base of the building should the bottom of the ladder be placed? A. 4.0 feet B. 8.0 feet C. 11.3 feet D. 16.0 feet 125. Robert leaves his home to go to his office. He drives 6 km due north and then 4 km due east. Approximately what is the shortest distance from Robert’s home to his office, in kilometers? A. 6.2 Trigonometry Page 61/91 B. 7.0 C. 7.2 D. 10.0 126. In the figure below, what is sin A. B. C. D. 127. In measures 90 degrees. Which statement must be true? A. B. Trigonometry Page 62/91 C. D. 128. In a right triangle, if tan , then what is sin x? A. B. C. D. 129. In and units. What is the length of the altitude from Vertex M? A. 25 sin 29° B. 25 tan 29° C. 25 sin 61° D. 25 tan 61° 130. In a right triangle, if Trigonometry , what is ? Page 63/91 A. B. C. D. 131. In a right triangle, if sin then what is tan x? A. B. C. D. 132. A right triangle has legs of lengths 1 cm and cm and a hypotenuse of length 2 cm. What must be the measures of its two non-right angles? A. 30° and 60° B. 45° and 45° C. 40° and 50° D. 35° and 55° Trigonometry Page 64/91 133. The figure below shows right triangles inside a rectangle. Based on the figure, which equation(s) are true? I. II. III. A. I only B. I and III only C. II and III only D. I, II, and III 134. Gary used landscape timbers to create a border around a garden shaped like a right triangle. The longest two timbers he used are 12 feet and 15 feet long. Which is closest to the length, in feet, of the shortest timber? A. 3 Trigonometry Page 65/91 B. 5.2 C. 7.3 D. 9 135. In a 30°-60°-90° triangle, the length of the hypotenuse is 12 inches. What is the length, in inches, of the side opposite the 60° angle? A. 6 B. C. D. 24 136. A company makes triangular flags as modeled in the diagram below. Which measurement is the closest approximation for the length x in inches? A. 7.5 B. 8.7 C. 10.6 Trigonometry Page 66/91 D. 15 137. The right triangles shown below are similar. Which equation involving is correct? A. B. C. D. 138. A circus elephant is being led up a 12-foot-long ramp to a trailer that is 4 feet above the ground. Trigonometry Page 67/91 Which equation could be used to find the angle between the ramp and the ground? A. B. C. D. 139. Which of the following is equal to cos 30°? A. cos 60° B. cos 90° C. sin 30° D. sin 60° 140. Jen is on the platform of her boat. She sights the top of a lighthouse at an angle of 30º as shown below. She knows that the height of the lighthouse is 50 meters. Trigonometry Page 68/91 How far is Jen from the base of the lighthouse, in meters? A. B. C. D. 141. Right triangle DEF is shown below with the dimensions given in units. Which measurement is closest to the value of x in units? A. 4.8 B. 5.1 C. 13.2 D. 14.9 Trigonometry Page 69/91 142. A right triangle is shown in the figure below. What is the value of x? A. 5 B. 10 C. 15 D. 20 143. If cos(180°) = –1, what is sin(180°)? A. –1 B. 0 C. 1 D. 2 144. Cleo is looking at an airplane flying at an altitude of 3 miles. Her angle of elevation is 37 degrees. About how far is the land distance from Cleo to the plane? Trigonometry Page 70/91 A. 2 miles B. 4 miles C. 5 miles D. 7 miles 145. A square tile with a side length of inches is cut diagonally. What is the length of the cut in inches? A. B. C. D. 146. Jeremy likes to ride his bike to his friend Khaleel’s house. If he takes the road, he rides 3.6 miles east and then 1.5 miles north. There is also a path that goes through the woods directly from Jeremy’s house to Khaleel’s house. Part A. To the nearest degree, what is the angle shown between the Trigonometry Page 71/91 road and the path? Use trigonometric functions to calculate the angle. Part B. To the nearest tenth of a mile, how much farther is it to go by the road than to go by the path? Show your work. Part C. One day Jeremy biked from his house to Khaleel’s house on the path, and then he returned by the road. He timed himself and found that it took the same amount of time both ways. On the road Jeremy rode at a speed of 13 miles per hour. To the nearest mile per hour, how fast was he going on the path through the woods? Explain your reasoning. Part D. Another path goes north off the road at a point 2.4 miles from Jeremy’s house. If Jeremy rode 2.4 miles on the road, turned onto the path going north, and then connected with the other path to go the rest of the way to Khaleel’s house, how far would he travel? Show your work and round your answer to the nearest tenth of a mile. Use words, numbers, and/or pictures to show your work. 147. Which statement is not true? A. B. C. Trigonometry Page 72/91 D. 148. Sina played basketball on a rectangular court that was 74 feet by 42 feet. After the game, she walked across the court diagonally from one corner to the opposite corner. Approximately what distance did Sina walk in feet? A. 58 B. 61 C. 85 D. 116 149. If cos(0) = 1, what is sin(0)? A. –1 B. 0 C. 1 D. 2 150. The measures of the sides of triangle ABC are a, b, and c. The height is h. Trigonometry Page 73/91 Part A. Based on the measures shown in the figure, what is the area of triangle ABC? Using the shaded right triangle, what is the sine of angle C? Based on the expression found for what is h? Substitute that value for h into the formula for the area of the triangle to give a formula for the area of the triangle. Part B. Instead of using the base and the height of a triangle to find the area, what would need to be known to find the area of a triangle using the formula you derived in Part A? Use words, numbers, and/or pictures to show your work. 151. A city park has three pavilions located within its boundaries. The locations of the pavilions and the distances, in meters, between them are shown in the diagram below. Which measurement is closest to the value of x, the distance between Pavilion #1 and Pavilion #3? A. 69 meters B. 87 meters C. 98 meters D. 109 meters Trigonometry Page 74/91 152. In shown below, the altitude from Point P to is designated l. Which equation can be used to find the area of the triangle, A, in terms of its side lengths and angle Q? A. B. C. D. 153. A pipe is to be installed to connect two water towers, located at Points A and B, as shown in the figure below. Trigonometry Page 75/91 The distance from Point C to the tower at Point A is 1.2 miles, while the distance from Point C to the tower at Point B is 1.8 miles. If what is the distance, to the nearest tenth of a mile, between the water towers? A. 1.5 B. 1.8 C. 2.0 D. 2.2 154. A parallelogram has sides 15 centimeters and 11 centimeters long with angles 130° and 50°. What is the approximate length of the longer diagonal of the parallelogram? A. 11.6 centimeters B. 15.4 centimeters C. 18.6 centimeters Trigonometry Page 76/91 D. 23.6 centimeters 155. Lori wants to derive the area formula, draws a perpendicular line segment from for to the base of In order to derive the formula, Lori A diagram of is shown below. Which equation could be used to derive the area formula for this triangle? A. B. C. D. 157. The magnitude of the resultant force, F, produced by two forces with magnitudes of 25 newtons and 40 newtons can be represented by the unknown length of the triangle shown below. What is the magnitude of F? Trigonometry Page 77/91 A. 41.3 newtons B. 47.2 newtons C. 52.4 newtons D. 65.0 newtons 158. A triangle and some of its dimensions are shown below. Which expression can be used to find the measure, in degrees, of A. B. C. D. 160. Sam is hiking on a trail. He leaves the trail and turns onto Path 1. Path 1 makes a 45° angle with the trail. After walking 300 meters (m) straight on Path 1, he turns 75° to Path 2, heading back toward the main trail, as shown in the figure. Assuming that the trail and the two paths are straight lines, approximately how far does Sam need to walk on Path 2 to get back to the trail? A. 212 m B. 245 m C. 424 m D. 580 m Trigonometry Page 78/91 163. Triangle JKL and some of its measurements are shown below. Which measurement is closest to the length of A. 11.0 cm B. 13.6 cm C. 14.2 cm D. 14.8 cm 164. Marcus wants to prove the Law of Sines: . He starts by drawing the triangle shown and the three altitudes. He uses the formula for the area of a triangle to write Which two substitutions are needed to show Trigonometry ? Page 79/91 . A. and B. and C. and D. and 166. Quadrilateral KLMN with diagonal If and is shown below. which is closest to the length of A. 6.2 cm B. 6.4 cm C. 6.9 cm Trigonometry Page 80/91 ? D. 7.2 cm 167. In Parallelogram PQRS, centimeters, centimeters, and centimeters as shown. What is the measure of Angle QPS to the nearest tenth of a degree? A. 48.4° B. 51.4° C. 60.7° D. 70.9° 169. Caleb placed an 8-foot ladder against his house. The base of the ladder was 2 feet away from the vertical side of the house along a straight downward-sloped surface, as shown in the diagram below. The measure of the angle between the ladder and the house is 14°. Which is closest to d, the distance from the base of the house to the point where the top of the ladder touches the house? A. 6.9 feet B. 7.3 feet C. 7.7 feet D. 8.3 feet Trigonometry Page 81/91 170. From a point at ground level 120 feet from the base of a building, the angle of elevation of the top of the building is 68°. What is the height, to the nearest foot, of the building? A. 111 B. 297 C. 320 D. 371 171. Bobby wants to calculate the area of shown below. Which formula can be used to calculate the area of A. B. C. D. Trigonometry Page 82/91 172. Mary wants to calculate the area of . What would be the first step in deriving the formula to calculate the area of A. draw B. draw C. draw D. draw 173. Two people, Julio and Marissa, are both looking at a plane in the sky to their east. From Julio's point of view, the plane is 87° from the horizontal ground. From Marissa's point of view, the plane is 88° from the horizontal ground. Julio and Marissa are 200 yards apart from each other. Trigonometry Page 83/91 How high is the plane above the ground, rounded to the nearest yard? A. 11,437 yards B. 11,444 yards C. 11,449 yards D. 11,453 yards 175. Triangle PQR has angles of 80°, 60°, and 40° as shown in the figure. Trigonometry Page 84/91 When QR = 14, which value is closest to the length of A. 7.0 B. 9.1 C. 10.5 D. 12.3 176. In and What is the length, to the nearest tenth of a unit, of A. 7.4 units B. 9.8 units C. 14.4 units D. 15.6 units 178. Cecelia is trying to find the length of She sets up the proportion Trigonometry Page 85/91 in triangle DEF shown below. Which statement best explains whether or not Cecelia’s method is correct? A. Cecelia is correct because she used the measures of the angles adjacent to and the correct proportions. B. Cecelia is not correct because she should have put 12 under and DF under C. Cecelia is not correct because she should have used the law of cosines. D. Cecelia is not correct because she should have used above DF. 186. Train A and Train B left a station at the same time, each traveling on straight paths that intersected to form a 60° angle with each other. After 30 minutes, Train A had traveled 20 miles and Train B had traveled 23 miles. What was the approximate distance between the trains at this time? A. 11.50 miles Trigonometry Page 86/91 B. 21.66 miles C. 26.44 miles D. 37.27 miles 189. In the triangle shown below, what is the measure of the smallest angle, rounded to the nearest degree? A. B. C. D. 190. Tom knows that the formula for the area of a triangle is For the following triangle, Tom knows the lengths of sides a, b, and c, along with the measures of angles A, B, and C, but he does NOT know the height (h). Trigonometry Page 87/91 Based on the values that Tom does know, how can he determine the height of the triangle? A. Find the sine ratio using angle B or angle C. B. Determine the average value of sides b and c. C. Find the cosine ratio using angle B or angle C. D. Determine the sum of all three sides and then divide by 3. 191. Samantha is estimating the width of a lake. She stands at Point B and looks through a long-range scope. She sees a boat shed at Point A that is about 9 miles away and a tall tree at Point C that is about 7 miles away. Which of the following is closest to the distance, in miles, across the lake from Point A to Point C? A. 9.7 B. 10.6 C. 11.4 D. 12.9 193. The Forest Service builds three rest stops at positions designated D, Y, and L, enclosing a triangular region. The distance DY is 5 miles, the distance LY is 8 miles, and What is the area of the enclosed region, to the nearest 0.1 square mile? Trigonometry Page 88/91 A. 10.6 B. 15.6 C. 25.0 D. 34.8 195. The locations of three baseball players are shown in the diagram below. Which measurement, in yards, is closest to the straight-line distance between Matthew and Troy? A. 14.1 B. 22.8 C. 25.5 D. 31.2 Trigonometry Page 89/91 197. In the triangle shown below, what is the measure, in degrees, of x, rounded to the nearest whole number? A. 57º B. 65º C. 77º D. 87º 198. A light pole is supported by two wires that extend from near the top of the pole and are anchored to stakes on either side of the pole. The wires meet at an angle of 72º. One of the wires forms an angle of 68º with the ground and has a length of 12 meters (m). Approximately how far apart are the two stakes that anchor the two wires to the ground? A. 12.31 m Trigonometry Page 90/91 B. 17.31 m C. 17.75 m D. 29.31 m Trigonometry Page 91/91