Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Regents Exam Questions A.A.43: Using Trigonometry to Find an Angle 1 Page 1 www.jmap.org Name: __________________________________ A.A.42: Trigonometric Ratios: Find the sine, cosine, and tangent ratios of an angle of a right triangle, given the lengths of the sides 1 The diagram below shows right triangle UPC. Which ratio represents the sine of 1) 2) 3) ? 4) 2 Which ratio represents in the right triangle shown below? 1) 2) 3) 4) Regents Exam Questions A.A.43: Using Trigonometry to Find an Angle 1 Page 2 www.jmap.org Name: __________________________________ 3 Which ratio represents in the accompanying diagram of 1) 2) 3) 4 In the accompanying diagram of right triangle ABC, . What is ? 1) 3) 2) 4) 5 The diagram below shows right triangle ABC. Which ratio represents the tangent of 1) 2) 3) 4) ? ? 4) , , , and Regents Exam Questions A.A.43: Using Trigonometry to Find an Angle 1 Page 3 www.jmap.org Name: __________________________________ 6 The diagram below shows right triangle LMP. Which ratio represents the tangent of 1) 2) 3) ? 4) 7 Right triangle ABC has legs of 8 and 15 and a hypotenuse of 17, as shown in the diagram below. The value of the tangent of is 1) 0.4706 2) 0.5333 3) 0.8824 4) 1.8750 8 In triangle MCT, the measure of Which ratio represents the sine of 1) 2) 3) 2) 3) , , and . 4) 9 In , the measure of the tangent of ? 1) , ? 4) , , and . Which ratio represents Regents Exam Questions A.A.43: Using Trigonometry to Find an Angle 1 Page 4 www.jmap.org Name: __________________________________ 10 Which equation shows a correct trigonometric ratio for angle A in the right triangle below? 1) 11 In 1) , 2) . If 2) 1 ANS: 2 REF: 010919ia 2 ANS: 1 REF: 011008ia 3 ANS: 1 REF: 080414a 4 ANS: 1 REF: 010316a 5 ANS: 2 REF: 081112ia 3) and 3) 4) , which statement is not true? 4) Regents Exam Questions A.A.43: Using Trigonometry to Find an Angle 1 Page 5 www.jmap.org Name: __________________________________ 6 ANS: 3 REF: 011226ia 7 ANS: 2 REF: 081026ia 8 ANS: 1 REF: fall0721ia 9 ANS: 2 REF: 061009ia 10 ANS: 3 REF: 011008ia 11 ANS: 4 If , then REF: 061224ia is the hypotenuse, and the triangle is a 3-4-5 triangle. A.A.44: Using Trigonometry to Find a Side: Find the measure of a side of a right triangle, given an acute angle and the length of another side 1 In the right triangle shown in the diagram below, what is the value of x to the nearest whole number? 1) 2) 3) 4) 12 14 21 28 Regents Exam Questions A.A.43: Using Trigonometry to Find an Angle 1 Page 6 www.jmap.org Name: __________________________________ 2 A tree casts a 25-foot shadow on a sunny day, as shown in the diagram below. If the angle of elevation from the tip of the shadow to the top of the tree is 32°, what is the height of the tree to the nearest tenth of a foot? 1) 13.2 2) 15.6 3) 21.2 4) 40.0 3 An 8-foot rope is tied from the top of a pole to a stake in the ground, as shown in the diagram below. If the rope forms a 57° angle with the ground, what is the height of the pole, to the nearest tenth of a foot? 1) 4.4 2) 6.7 3) 9.5 4) 12.3 4 A right triangle contains a 38° angle whose adjacent side measures 10 centimeters. What is the length of the hypotenuse, to the nearest hundredth of a centimeter? 1) 7.88 2) 12.69 3) 12.80 4) 16.24 Regents Exam Questions A.A.43: Using Trigonometry to Find an Angle 1 Page 7 www.jmap.org Name: __________________________________ 5 As shown in the diagram below, a ladder 5 feet long leans against a wall and makes an angle of 65° with the ground. Find, to the nearest tenth of a foot, the distance from the wall to the base of the ladder. 6 A stake is to be driven into the ground away from the base of a 50-foot pole, as shown in the diagram below. A wire from the stake on the ground to the top of the pole is to be installed at an angle of elevation of 52°. How far away from the base of the pole should the stake be driven in, to the nearest foot? What will be the length of the wire from the stake to the top of the pole, to the nearest foot? Regents Exam Questions A.A.43: Using Trigonometry to Find an Angle 1 Page 8 www.jmap.org Name: __________________________________ 7 A hot-air balloon is tied to the ground with two taut (straight) ropes, as shown in the diagram below. One rope is directly under the balloon and makes a right angle with the ground. The other rope forms an angle of 50º with the ground. Determine the height, to the nearest foot, of the balloon directly above the ground. Determine the distance, to the nearest foot, on the ground between the two ropes. 1 ANS: 3 REF: 010912ia 2 ANS: 2 REF: 080914ia 3 ANS: 2 REF: 061108ia 4 ANS: 2 Regents Exam Questions A.A.43: Using Trigonometry to Find an Angle 1 Page 9 www.jmap.org Name: __________________________________ REF: 081126ia 5 ANS: 2.1. REF: 011133ia 6 ANS: 39, 63. . REF: 060937ia 7 ANS: 84, 71 REF: 081039ia 1 In the accompanying diagram of right triangle ABC, and Which single function could be used to find AB? 1) 2) 3) 4) 2 In right triangle ABC, . Which equation is true for this triangle? 1) 2) 3) 4) . Regents Exam Questions A.A.43: Using Trigonometry to Find an Angle 1 Page 10 www.jmap.org Name: __________________________________ 3 The accompanying diagram shows a ramp 30 feet long leaning against a wall at a construction site. If the ramp forms an angle of 32° with the ground, how high above the ground, to the nearest tenth, is the top of the ramp? 1) 15.9 ft 2) 18.7 ft 3) 25.4 ft 4) 56.6 ft 4 The tailgate of a truck is 2 feet above the ground. The incline of a ramp used for loading the truck is 11°, as shown below. Find, to the nearest tenth of a foot, the length of the ramp. 5 Joe is holding his kite string 3 feet above the ground, as shown in the accompanying diagram. The distance between his hand and a point directly under the kite is 95 feet. If the angle of elevation to the kite is 50°, find the height, h, of his kite, to the nearest foot. Regents Exam Questions A.A.43: Using Trigonometry to Find an Angle 1 Page 11 www.jmap.org Name: __________________________________ 6 A surveyor needs to determine the distance across the pond shown in the accompanying diagram. She determines that the distance from her position to point P on the south shore of the pond is 175 meters and the angle from her position to point X on the north shore is 32°. Determine the distance, PX, across the pond, rounded to the nearest meter. 7 Find, to the nearest tenth of a foot, the height of the tree represented in the accompanying diagram. 8 In the accompanying diagram, x represents the length of a ladder that is leaning against a wall of a building, and y represents the distance from the foot of the ladder to the base of the wall. The ladder makes a 60° angle with the ground and reaches a point on the wall 17 feet above the ground. Find the number of feet in x and y. Regents Exam Questions A.A.43: Using Trigonometry to Find an Angle 1 Page 12 www.jmap.org Name: __________________________________ 9 In the accompanying diagram, a ladder leaning against a building makes an angle of 58º with level ground. If the distance from the foot of the ladder to the building is 6 feet, find, to the nearest foot, how far up the building the ladder will reach. 10 As shown in the accompanying diagram, a ladder is leaning against a vertical wall, making an angle of 70° with the ground and reaching a height of 10.39 feet on the wall. Find, to the nearest foot, the length of the ladder. Find, to the nearest foot, the distance from the base of the ladder to the wall. 11 From a point on level ground 25 feet from the base of a tower, the angle of elevation to the top of the tower is 78°, as shown in the accompanying diagram. Find the height of the tower, to the nearest tenth of a foot. Regents Exam Questions A.A.43: Using Trigonometry to Find an Angle 1 Page 13 www.jmap.org Name: __________________________________ 12 A lighthouse is built on the edge of a cliff near the ocean, as shown in the accompanying diagram. From a boat located 200 feet from the base of the cliff, the angle of elevation to the top of the cliff is 18° and the angle of elevation to the top of the lighthouse is 28°. What is the height of the lighthouse, x, to the nearest tenth of a foot? 1 ANS: 1 2 ANS: 4 3 ANS: 1 PTS: 2 4 ANS: PTS: 2 REF: PTS: 2 010926a REF: 018933siii REF: 080724a 10.5. PTS: 2 5 ANS: REF: spring9825a 116. PTS: 4 6 ANS: REF: 069934a 109. PTS: 3 7 ANS: REF: 060030a Regents Exam Questions A.A.43: Using Trigonometry to Find an Angle 1 Page 14 www.jmap.org Name: __________________________________ 28.2. PTS: 4 8 ANS: REF: 010135a . PTS: 4 9 ANS: REF: 080231a 10. PTS: 2 REF: 010531a 10 ANS: Length of ladder = 11 and distance from the base of the ladder to the wall = 4. . PTS: 4 11 ANS: REF: 010638a 117.6. PTS: 2 12 ANS: REF: 010735a 41.4. PTS: 4 REF: 010837a Regents Exam Questions A.A.43: Using Trigonometry to Find an Angle 1 Page 15 www.jmap.org Name: __________________________________ 1 The angle of elevation from a point 25 feet from the base of a tree on level ground to the top of the tree is 30°. Which equation can be used to find the height of the tree? 1) 2) 3) 4) 2 In right triangle ABC, , , and . What is the length of the hypotenuse? 1) 2) 3) 8 4) 3 A 10-foot ladder is to be placed against the side of a building. The base of the ladder must be placed at an angle of 72° with the level ground for a secure footing. Find, to the nearest inch, how far the base of the ladder should be from the side of the building and how far up the side of the building the ladder will reach. 4 Draw and label a diagram of the path of an airplane climbing at an angle of 11° with the ground. Find, to the nearest foot, the ground distance the airplane has traveled when it has attained an altitude of 400 feet. 5 A tree casts a shadow that is 20 feet long. The angle of elevation from the end of the shadow to the top of the tree is 66°. Determine the height of the tree, to the nearest foot. Regents Exam Questions A.A.43: Using Trigonometry to Find an Angle 1 Page 16 www.jmap.org Name: __________________________________ 6 A person measures the angle of depression from the top of a wall to a point on the ground. The point is located on level ground 62 feet from the base of the wall and the angle of depression is 52°. How high is the wall, to the nearest tenth of a foot? 7 A ship on the ocean surface detects a sunken ship on the ocean floor at an angle of depression of 50°. The distance between the ship on the surface and the sunken ship on the ocean floor is 200 meters. If the ocean floor is level in this area, how far above the ocean floor, to the nearest meter, is the ship on the surface? 8 At Mogul’s Ski Resort, the beginner’s slope is inclined at an angle of 12.3°, while the advanced slope is inclined at an angle of 26.4°. If Rudy skis 1,000 meters down the advanced slope while Valerie skis the same distance on the beginner’s slope, how much longer was the horizontal distance that Valerie covered? 1) 81.3 m 2) 231.6 m 3) 895.7 m 4) 977.0 m 1 ANS: 1 2 ANS: 3 3 ANS: 114” and 37”. REF: 080033a 4 ANS: 2,058. REF: 060419a REF: 088725siii . Regents Exam Questions A.A.43: Using Trigonometry to Find an Angle 1 Page 17 www.jmap.org Name: __________________________________ REF: 010235a 5 ANS: 45. REF: 080536a 6 ANS: 79.4. REF: 060639a 7 ANS: 153. REF: 080133a 8 ANS: 1 REF: 080108b Regents Exam Questions A.A.43: Using Trigonometry to Find an Angle 1 Page 18 www.jmap.org Name: __________________________________ A.A.43: Using Trigonometry to Find an Angle: Determine the measure of an angle of a right triangle, given the length of any two sides of the triangle 1 Which equation could be used to find the measure of one acute angle in the right triangle shown below? 1) 2) 3) 4) 2 In the diagram of shown below, and . To the nearest tenth of a degree, what is the measure of the largest acute angle in the triangle? 1) 32.0 2) 38.7 3) 51.3 4) 90.0 3 In right triangle ABC shown below, What is the measure of 1) 31.5 2) 37.7 3) 52.3 4) 58.5 and . , to the nearest tenth of a degree? Regents Exam Questions A.A.43: Using Trigonometry to Find an Angle 1 Page 19 www.jmap.org Name: __________________________________ 4 The center pole of a tent is 8 feet long, and a side of the tent is 12 feet long as shown in the diagram below. If a right angle is formed where the center pole meets the ground, what is the measure of angle A to the nearest degree? 1) 34 2) 42 3) 48 4) 56 5 A communications company is building a 30-foot antenna to carry cell phone transmissions. As shown in the diagram below, a 50-foot wire from the top of the antenna to the ground is used to stabilize the antenna. Find, to the nearest degree, the measure of the angle that the wire makes with the ground. 6 In right triangle ABC, degree, the measure of , , , and . Find, to the nearest . 7 A 28-foot ladder is leaning against a house. The bottom of the ladder is 6 feet from the base of the house. Find the measure of the angle formed by the ladder and the ground, to the nearest degree. Regents Exam Questions A.A.43: Using Trigonometry to Find an Angle 1 Page 20 www.jmap.org Name: __________________________________ 8 A trapezoid is shown below. Calculate the measure of angle x, to the nearest tenth of a degree. 9 In right triangle ABC shown below, inches, inches, and Find the number of degrees in the measure of angle BAC, to the nearest degree. Find the length of to the nearest inch. . Regents Exam Questions A.A.42: Trigonometric Ratios 1 www.jmap.org 1 ANS: 1 2 ANS: 3 REF: 080824ia . A 90º angle is not acute. REF: 080829ia 3 ANS: 1 4 ANS: 2 REF: 061114ia REF: 060816ia 5 ANS: REF: 061033ia 6 ANS: 53. REF: 011032ia 7 ANS: 78. REF: 061235ia 8 ANS: 41.8. REF: 081135ia 9 ANS: 54, 23. . REF: 081238ia A.A.43: Using Trigonometry to Find an Angle: Determine the measure of an angle of a right triangle, given the length of any two sides of the triangle Regents Exam Questions A.A.42: Trigonometric Ratios 1 www.jmap.org 1 Cassandra is calculating the measure of angle A in right triangle ABC, as shown in the accompanying diagram. She knows the lengths of and , If she finds the measure of angle A by solving only one equation, which concept will be used in her calculations? 1) Pythagorean theorem 2) 3) 4) 2 Ron and Francine are building a ramp for performing skateboard stunts, as shown in the accompanying diagram. The ramp is 7 feet long and 3 feet high. What is the measure of the angle, x, that the ramp makes with the ground, to the nearest tenth of a degree? 3 A person standing on level ground is 2,000 feet away from the foot of a 420-foot-tall building, as shown in the accompanying diagram. To the nearest degree, what is the value of x? 4 If a tree 28 meters tall casts a shadow 32 meters long, what is the angle of elevation of the Sun to the nearest degree? 1) 29 2) 41 3) 50 4) 61 Regents Exam Questions A.A.42: Trigonometric Ratios 1 www.jmap.org 5 As seen in the accompanying diagram, a person can travel from New York City to Buffalo by going north 170 miles to Albany and then west 280 miles to Buffalo. If an engineer wants to design a highway to connect New York City directly to Buffalo, at what angle, x, would she need to build the highway? Find the angle to the nearest degree. To the nearest mile, how many miles would be saved by traveling directly from New York City to Buffalo rather than by traveling first to Albany and then to Buffalo? 6 In the accompanying diagram, the base of a 15-foot ladder rests on the ground 4 feet from a 6-foot fence. a If the ladder touches the top of the fence and the side of a building, what angle, to the nearest degree, does the ladder make with the ground? b Using the angle found in part a, determine how far the top of the ladder reaches up the side of the building, to the nearest foot. 7 The accompanying diagram shows a flagpole that stands on level ground. Two cables, r and s, are attached to the pole at a point 16 feet above the ground. The combined length of the two cables is 50 feet. If cable r is attached to the ground 12 feet from the base of the pole, what is the measure of the angle, x, to the nearest degree, that cable s makes with the ground? Regents Exam Questions A.A.42: Trigonometric Ratios 1 www.jmap.org 1 ANS: 4 2 ANS: PTS: 2 REF: 060820a 25.4. PTS: 2 3 ANS: REF: 060735a 12. PTS: 3 4 ANS: 2 5 ANS: REF: 089927a PTS: 2 59, 122. . REF: 068533siii . The trip from New York City to Buffalo via Albany is 450 (280 + 170) miles. Therefore traveling directly to Buffalo would save (450 – 328) 122 miles. PTS: 4 6 ANS: 56, 12. PTS: 4 7 ANS: 32. PTS: 4 REF: 060231a . REF: 010438a . If the combined length of the two cables is 50 feet, then s is 30 (50 – 20) feet. REF: 060539a