Download TMA Assignment List - Triangle Trig

 Trig/Math Anal Name_______________________No_____ LATE AND ABSENT HOMEWORK IS ACCEPTED UP TO THE TIME OF THE CHAPTER TEST ON _____
HW NO. TT‐1 SECTIONS 12‐5 TT‐2 12‐6 TT‐3 12‐7 TT‐4 12‐8 & Application Problems TT‐5 12‐9 Application Problems TT‐6 12‐3 TT‐7 Review ASSIGNMENT Practice Set D Practice Set E Practice Set F Practice Set G Practice Set A #1, 2 Practice Set H Practice Set J Practice Set K #1, 3, 5, 7, 9, 16 Practice Set L #3, 9 Practice Set M #5, 9, 13 Practice Set B Practice Set K #12 Practice Set L #8 Practice Set M #1, 3 Practice Set N Practice Set P #26, 27, 37, 38 Practice Set A #3, 4 Practice Set C Practice Set P #28, 29, 31, 41, 43 Practice Set M #10 √ DUE Practice Set A Solve the triangle, given: 1. a = 6, b = 9.3, c = 13 3. m∠A = 34, a = 4, b = 6 (Two triangles) 4. Find the area and perimeter of a 12‐gon inscribed in a circle with radius=14. Practice Set B: Application Problems 1. Find the area of a regular octagon inscribed in a circle of radius 40 cm. 2. Adjacent sides of a parallelogram have lengths 6 cm and 7 cm, and the measure of the included angle is 30°. Find the area of the parallelogram. 3. A ship passes by buoy B which is known to be 3,000 yards from peninsula P. The ship is steaming east along line BE and ∠PBE is measured as 28°. After 10 minutes, the ship is at S and ∠PSE is measured as 63°. a. How far from the peninsula is the ship when it is at S? b. If the ship continues east, what is the closest it will get to the peninsula? (Hint: the closest distance is the perpendicular.) c. How fast (in yd/min) is the ship traveling? d. Ship speeds are often given in knots, where 1 knot = 1 nautical mile per hour ≈ 6080 feet per hour. Convert your answer in part c to knots. TMA Assignment List - Triangle Trig Page 1
2. m∠A = 52, m∠B = 84, c = 12 4. From points P and Q, 180 m apart, a tree at T is sighted on the opposite side of a deep ravine. From point P, a compass indicates that the angle between the north‐south line and line of sight PT is 27° and that the angle between the north‐south line and PQ is 78°. From point Q, the angle between the north‐south line and QT is 43°. a. How far from P is the tree? b. How far from P is the point on PQ that is closest to the tree? 5. An isosceles trapezoid has a height of 4 cm and bases 3 cm and 7 cm long. How long are its diagonals? 6. Two airplanes, at points A and B in the diagram, have elevations of 23,000 ft and 18,000 ft, respectively. Both are flying east toward an airport control tower at T. From T, the angle of elevation of the airplane at A is 4°, and the angle of elevation of the airplane at B is 2.5°. How far apart (in miles) are the airplanes? (5,280 ft = 1 mi). 7. An airplane at A is flying at a height of 6 mi above Earth’s surface at S, as shown. a. Find the distance to the nearest tenth of a mile from A to the horizon H (The radius of Earth is about 4,000 miles.) b. Find the curved distance to the nearest tenth of a mile from S along Earth’s surface to H. Practice Set C: Review 1. In ΔABC , m∠A = 70, m∠C = 40, c = 5 . Find 2. Find the measure of the smallest angle and the area of a triangle with sides 5, 6, and 7. the length of side a 4. Find the area of a triangle with sides 10, 6, 3. In ΔABC , b = 10, c = 5, m∠A = 32 , find the and 14 length of side a 5. Adjacent sides of a parallelogram have 6. What is the angle of elevation of the sun lengths 6 cm and 8 cm, and the measure of the when a flagpole 27.5 m high casts a shadow 42 included angle is 35°. Find the area of the m long? parallelogram. 7. A kite 6 m long is a quadrilateral having two 8. Two planes leave an airport at the same sides each 3 m long and two sides each 4.5 m time, one flying due south at 400 mph, and the long. How wide is the kite? (That is, what is other flying due northwest at 450 mph. How the length of the shorter diagonal?) far apart are they three hours later? Practice Set D: Solving Right Triangles (Page 542) TMA Assignment List - Triangle Trig Page 2
Give lengths to three significant digits and angle measures to the nearest tenth of a degree or nearest ten minutes. Solve each right triangle ABC. 1. ∠A = 28.6°, c = 145 3. ∠B = 71.5°, a = 1.82 7. a = 460, c = 640 2. ∠B = 42.8°, c = 16.3 4. ∠A = 57.5°, b = 355 17. The height of an isosceles triangle is 10 units and its base is 16 units long. Find its angles. 18. The height of an isosceles trapezoid is 12 units and its bases have lengths 25 and 15 units. Find its angles. 19b. Find the perimeter of a regular pentagon circumscribed about a unit circle. 19a. Find the perimeter of a regular pentagon inscribe in a unit circle (a circle with radius 1). 20a. Repeat exercise 19a for a regular polygon having 10 sides. 20b. Repeat exercise 19b for a regular polygon having 10 sides. Practice Set E: Solving Right Triangles Problems (Page 543) Give lengths to three significant digits and angle measures to the nearest tenth of a degree. 1. What is the angle of elevation of the sun 3. In one minute a plane descending at a when a flagpole 22.5 m high casts a shadow constant angle of depression of 11.5° travels 1500 m along its line of flight. How much 32.4 m long? altitude has it lost? 5. A television camera on a blimp is focused on 7. Opposite corners of a small rectangular park a football field with angle of depression 18.3° . are joined by diagonal paths, each 240 m long. A range finder on the blimp determines that Find the dimensions of the park if the paths the field is 1850 m away. How high is the intersect at a 36° angle. blimp? 9. From a point 100 m from a building, the 11. Two boats are in line with a tower whose angles of elevation of the top and bottom of a top is 48 m above the water. How far apart are flagpole atop the building are 62.2° and 59.5° . the boats if their angles of depression from the How tall is the flagpole? top of the tower are 23.5° and 27.5° ? TMA Assignment List - Triangle Trig Page 3
13. Two observers 1600 m apart on a straight road measure the angles of elevation of a helicopter hovering over the road between them. If these angles are 32.0° and 50.5° , how high is the helicopter? Practice Set F: Law of Cosines (Page 548) Find lengths to three significant digits and angles to the nearest tenth of a degree. Find the indicated part of ΔABC 1. a = 5, b = 7, ∠C = 40°, c = 3. c = 11, a = 12, ∠B = 81°, b = 5. c = 20, b = 30, ∠A = 140°, a = 7. a = 7, b = 9, c = 12, ∠B = 9. a = 12, b = 10, c = 18, largest angle = 11. a = 0.6, b = 0.8, c = 1.2, smallest angle = 13. Find the lengths of the sides of a parallelogram whose diagonals intersect at a 35° angle and have lengths 6 and 10. (Recall that the diagonals of a parallelogram bisect each other). Practice Set G: Law of Cosines Problems (Page 549) Find lengths to three significant digits and angles to the nearest tenth of a degree. 1. Two planes leave an airport at the same 3. A cruise ship and a freighter leave port at time, one flying due east at 600 km/h, and the the same time and travel straight‐line courses other flying due northwest at 400 km/h. How at 30 km/h and 10 km/h, respectively. Two far apart are they two hours later? (hint: To hours later they are 50 km apart. What is the work with smaller numbers, use 100 km as the angle between their courses? length unit.) 4. A baseball diamond is a square 90 feet on a 7. A vertical pole 20 m tall standing on a side, and the pitcher’s mound is 60.5 feet from 15° slope is to be braced by two cables home plate. How far is it from the mound to extending from the top of the pole to the first base? points on the ground, 30 m up the slope and 30 m down the slope. How long must the cables be? Practice Set H: Law of Sines (Page 552) Find the indicated part of ΔABC to three significant digits or to the nearest tenth of a degree. If there are two solutions, give both of them. 1. a = 16, ∠A = 35°, ∠B = 65°, b = 3. b = 2.10, ∠A = 110°, ∠C = 40°, a = 5. c = 30, ∠A = 42°, ∠C = 98°, b = 7. a = 20, b = 15, ∠A = 40°, ∠B = 9. a = 2.0, c = 3.2, ∠C = 125°, ∠B = Practice Set J: Law of Sines Problems (Page 553) Give answers to three significant digits. 1. Two angles of a triangle are 25° and 60° , 2. How long is the base of an isosceles triangle and the longest side is 45 m. Find the length of if each leg is 35 cm long and each base angle the shortest side. measures 18° ? 8. A pilot approaching a 10,000‐foot runway 4. A parcel of land is in the shape of an finds that the angles of depression of the ends isosceles triangle. The base fronts on a road of the runway are 12° and 15° . How far is the and has a length of 641 ft. If the legs meet at an angle of 29° , how long are they? plane from the nearer end of the runway? Practice Set K: Solving General Triangles (Page 558) TMA Assignment List - Triangle Trig Page 4
Give lengths to three significant digits and angle measures to the nearest tenth of a degree. Solve the triangles. If there are two solutions, find both. If there are no solutions, so state. Find the area of each triangle for questions #1‐7. 1. a = 15, ∠B = 30°, ∠C = 50° 3. a = 4, b = 7, c = 9 5. b = 12, c = 15, ∠A = 100° 7. a = 30, b = 20, ∠A = 130° 9. a = 12, b = 7, ∠B = 35° (Two triangles) 16. Find the lengths of the diagonals of the quadrilateral shown. 12. b = 15, c = 13, ∠C = 50° b=15 (Two triangles) Practice Set L: Solving General Triangles Problems (Page 559‐560) Given lengths to three significant digits and angle measures to the nearest tenth of a degree. 3. A television antenna, standing on level ground, is supported by two cables, extending from the top of the antenna to the ground on opposite sides of the antenna. One cable is 300 m long and makes an angle of 48° with the ground. The other cable is 270 m long. Find the acute angle that the second cable makes with the ground and the distance between the cables at the ground.
8. A kite 2.5 m long is a quadrilateral having two sides each 1 m long and two sides each 2 m long. How wide is the kite? (That is, what is the length of the shorter diagonal?) 9. From the top of a tower 80 m above sea level, an observer sights a sailboat at an angle of depression of 9° . Turning in a different direction he sights another sailboat at an angle of depression of 12° . The angle between these lines of sight is 36° . How far apart are the boats? Practice Set M: Areas of Triangles (Page 563) Find the areas of the triangles described. Give answers to three significant digits. 1. ∠A = 30°, ∠B = 45°, b = 20 3. b = 4, c = 18, ∠A = 32° 5. a = 5, b = 12, c = 10 9. Find the area of a parallelogram that has a 65° angle and sides with lengths 8 and 12. 10. Find the area of a rhombus that has 13. Find the area of a regular pentagon whose perimeter 60 and an angle of 50° sides are 10 cm long. Practice Set N: Trig Functions of General Angles (Page 531) Give the reference angle α for each angle θ 1. 2. 3. 4. 5. θ = 260° 7. θ = 185° TMA Assignment List - Triangle Trig Page 5
6. θ = 175° 8. θ = −60° 9. θ = −350° 10. θ = −100° 11. θ = 500° 12. θ = 400° State the values of the six trigonometric functions of θ . If a value is undefined, so state. 13. 14. 15. Practice Set P: Trig Functions of General Angles (Page 533) Give the exact values of the six trigonometric functions of the given angle. Use radicals when necessary. 26. 300° 27. 150° 28. −45° 29. 330° 31. −300° 12
3
37. cos θ = − , 0° < θ < 180° 38. sin θ = − , cos θ > 0 13
5
a. Give the quadrant of angle θ a. Give the quadrant of angle θ b. Find the five other trigonometric functions b. Find the five other trigonometric functions of θ . When radicals occur, leave your answer of θ . When radicals occur, leave your answer in simplest radical form. in simplest radical form. 2
3
41. cos θ = , 0° < θ < 270° 43. sin θ = − , tan θ > 0 3
4
a. Give the quadrant of angle θ a. Give the quadrant of angle θ b. Find the five other trigonometric functions b. Find the five other trigonometric functions of θ . When radicals occur, leave your answer of θ . When radicals occur, leave your answer in simplest radical form. in simplest radical form. ANSWERS Practice Set A m∠A = 24.8, m∠B = 40.6,
m∠C = 44,
m∠B = 57, m∠C = 89, c = 7.2
4. 588 1.
2. 3. m∠C = 114.6
a = 13.6, b = 17.2
m∠B = 123, m∠C = 23, c = 2.8
Practice Set B 1. 4525 2. 21 3a. 1581 yds 3b. 1407 yds 3c. 193 yds/min 3d. 5.7 knots 4a. 164.2 4b. 103.3 5. 6.4 6. 16 miles 7a. 219 mi. 7b. 209 mi. Practice Set C 1. 7.3 2. 44.4°,14.7 3. 6.3 4. 26 5. 27.5 2 6. 33.2 7. 4.4 8. 2,357 Practice Set D 1. a = 69.4, b = 127, m∠B = 61.4° 2. a = 12.0, b = 11.1, m∠A = 47.2° 3. b = 5.44, c = 5.74, m∠A = 18.5° 4. a = 557, c = 661, ∠B = 32.5° 7. b = 445, m∠A = 46.0°, m∠B = 44.0° 17. 51.3°,51.3°, 77.4° TMA Assignment List - Triangle Trig Page 6
18. 67.4°, 67.4°,1126.°,112.6° 19a. 5.88 19b. 7.27 20a. 6.18 20b. 6.50 Practice Set E 1. 34.8° 3. 299 m 5. 581 m 7. 228 m by 74.2 m 9. 19.9 m 11. 18.2 m or 203 m 13. 660 m Practice Set F 1. 4.51 3. 15.0 5. 47.1 7. 48.2 9. m∠C = 109.5 11. m∠A = 26.4 13. 3.07, 7.65 Practice Set G 1. 1850 km 2. 51.3° 4. 63.7 ft. 7. 40.1 m and 31.5 Practice Set H 1. 25.3 3. 3.95 5. 19.5 7. 28.8 9. 24.2 Practice Set J 1. 19.1 m 2. 66.6 cm 4. 1280 ft. 8. 39,800 ft. Practice Set K 1. area = 43.3, ∠A = 100 , b = 7.62, c = 11.7 3. area=13.4, ∠A = 25.2, ∠B = 48.2, ∠C = 106.6
5. area=88.6, ∠B = 34.7, ∠C = 45.3, a = 20.8 7. area=99.5, ∠B = 30.7, ∠C = 19.3, c = 12.9 9. ∠A = 79.5, ∠C = 65.5, c = 11.1 or ∠A = 100.5, ∠C = 44.5, c = 8.55 12. ∠B = 62.1°, ∠A = 67.9°, a = 15.7 or ∠B = 117.9°, ∠A = 12.1°, a = 3.56 16. 2.62 and 1.35 Practice Set L 3. 55.7°,353m 8. 1.52 m 9. 302 m Practice Set M 1. 137 3. 19.1 5. 24.5 9. 87.0 10. 172 13. 172 Practice Set N 1. 45° 2. 60° 3. 30° 4. 45° 5. 80° 6. 5° 7. 5° 8. 60° 9. 10° 10. 80° 11. 40° 12. 40° 3
3
4
4
sin θ = 5 , cos θ = − 5
sin θ = − 5 , cos θ = 5
sin θ = 22 , cos θ = 22
13. tan θ = − 34 , csc θ = 53 14. tan θ = − 43 , csc θ = − 54 15. tan θ = 1, csc θ = 2 sec θ = − 54 , cot θ = − 34
sec θ = 53 , cot θ = − 34
sec θ = 2, cot θ = 1
Practice Set P sin ( 300° ) = −
3
2
, cos ( 300° ) = 12 ,
sin (150° ) = 12 , cos (150° ) = −
26. tan ( 300° ) = − 3, csc ( 300° ) = − 2 3 , 3
sec ( 300° ) = 2, cot ( 300° ) = −
28. sin ( −45° ) = −
2
2
27. tan (150° ) = − 3 , csc (150° ) = 2,
3
sin ( 330° ) = − 12 , cos ( 330° ) =
2
2
3
2
,
, tan ( −45° ) = −1 29. tan ( 330° ) = − 33 , csc ( 330° ) = −2, csc ( −45° ) = − 2,sec ( −45° ) = 2, cot ( −45° ) = −
TMA Assignment List - Triangle Trig Page 7
,
sec (150° ) = − 2 3 3 , cot (150° ) = − 3
3
3
, cos ( −45° ) =
3
2
sec ( 330° ) =
2 3
3
, cot ( 330° ) = − 3
sin ( −300° ) =
3
2
, cos ( −300° ) = 12 ,
31. tan ( −300° ) = 3, csc ( −300° ) = 2 3 , 3
sec ( −300° ) = 2, cot ( −300° ) =
38a. 4 3
3
37a. 2 sin θ = 135 ,
37b. tan θ = − 5 , csc θ = 13 , 12
5
13
sec θ = − 12
, cot θ = − 125
41a. 1 cos θ = ,
sin θ =
5
3
,
41b. tan θ =
5
2
, csc θ = 3 5 5 , 4
5
38b. tan θ = − 3 , csc θ = − 5 , 4
3
sec θ = , cot θ = −
5
4
4
3
sec θ = 32 , cot θ =
43a. 3 cos θ =
− 7
4
,
43b. tan θ = 3 7 , csc θ = − 4 , 7
3
sec θ = − 4 7 7 , cot θ =
TMA Assignment List - Triangle Trig Page 8
7
3
2 5
5
SPIRAL REVIEW (CLASSWORK) Lesson TT‐2 Classwork 12‐5 Find the measure of the angles of an
isosceles triangle with an altitude of 11 and a
base of 14. Lesson TT‐3 Classwork 12‐5 Find the length of the perimeter of a
12‐6 Find the measure of the smallest angle in
regular pentagon inscribed in a circle of radius
ΔABC if a = 30, b = 20, c = 40 3. Lesson TT‐4 Classwork 12‐5 Find the length of the perimeter of a
12‐6 In ΔABC , find c if a = 5, b = 7 and
regular pentagon inscribed in a circle of radius
∠C = 40° . 5. 12‐7 Solve ΔABC if
m∠B = 118, m∠C = 36, c = 14 Lesson TT‐5 Classwork 12‐5 Find the measure of the angles of an
12‐6 An observer located 3 km from a rocket
isosceles triangle with an altitude of 15 and a
launch site sees a rocket at an angle of elevation
base of 11. of 23° . How high is the rocket at that moment? 12‐8 Solve ΔABC given
12‐7 Find the area of ΔABC if
a = 22, c = 19, m∠B = 81 m∠B = 30, b = 16, c = 25 (there are 2 triangles). Lesson TT‐6 Classwork 12‐5 Opposite corners of a small rectangular
12‐6 A news blimp hovers over a stadium at an
park are joined by diagonal paths, each 180 m
altitude of 135 m. The pilot sights an
long. Find the dimensions of the park if the
elementary school at a 10° angle of depression.
paths intersect at a 32° angle. Find the ground distance between the stadium
and the school. 12‐7 Two angles of a triangle are 35° and 50° , 12‐8 Find the area of ΔABC if
and the longest side is 50 m. Find the length of a = 22, b = 20, c = 19 the shortest side. 12‐9 Find the area of a regular octagon
inscribed in a circle of radius 40 cm. TMA Assignment List - Triangle Trig Page 9