Name: Date: Period Trigonometry Applications Draw a picture (if one is not provided), write an equation, and solve each problem. Round answers to the nearest hundredths. 1. A 110-ft crane set at an angle of 45 to the horizontal can raise building material to what height? 2. The angle of elevation from a ship to the top of the lighthouse is 3. If the ship is 1000m from the lighthouse, how tall is the lighthouse? 3. A ship s pilot knows that a building on the coast is 100m tall. If he finds the angle of elevation to be 2, how far is the ship from the coastline? 4. A kite string is 60m long and makes an angle of 42 with ground. How high above the ground is the kite? 5. What is the angle of elevation of the sun when a tower 200 feet high casts a shadow 80ft long? 6. An airplane takes off at an angle of 15 with the ground. What is the distance it has flown when it has covered a horizontal distance of 1800 feet? 7. From the top of a tower, the angle of depression to a stake on the ground is 72. The top of the tower is 80ft above ground. How far is the stake from the foot of the tower? 8. A tree 40ft high casts a shadow 58ft long. Find the measure of the angle of elevation of the sun. 9. A ladder leaning against a house makes an angle of 60 with the ground. The foot of the ladder is 7 feet from the foundation of the house. How long is the ladder? 10. A balloon on a 40-foot string makes an angle of 50 with the horizontal (because the kid is running). How high above the ground is the balloon if the hand of the person holding the balloon is 6 feet above the ground?
11. A cable is used to support a 245-m television tower. If the angle the cable makes with the ground is 78, how long is the cable? 12. A monument casts a shadow 215ft long when the angle of elevation of the sun is 52. Find the height of the monument. 13. The angle of depression of a tree from the top of the monument in problem 12 is 78. How far is the tree from the base of the monument? 14. The angle of depression of a car from an air balloon basket is 40. The balloon is directly over a water tower that is 5km from the car. Find the altitude of the balloon. 15. A person on a building 180ft high looked at a bench in a park below. The angle of depression was 24. How far is the bench from the foot of the building? 16. The length of a guywire supporting a radio tower is 175ft. The angle of elevation of the top of the radio tower from the foot of the guywire is 65. How tall is the tower? 17. A flagpole is at the top of a building. Four hundred feet from the base of the building, the angle of elevation of the top of the pole is 22, and the angle of elevation of the bottom of the pole is 20. Find the height of the flagpole. 18. The Chrysler Building in New York is 1046ft tall. A person stands half a mile away and views the top of the building. Find the angle of elevation of the top. (5280 feet = 1 mile) 19. A Mission Control observer, 4.5km from the launch pad, observes a space shuttle ascending. The angle of elevation of the shuttle is 38. How far (air distance) is the shuttle form the observer? 20. A television tower 150ft high casts a shadow 200ft long. Find the angle of elevation of the sun. 21. A ramp is 120ft long and rises vertically 15ft. Find the angle of the elevation of the ramp.
22. The base of an isosceles triangle has length of 16 and measure of the vertex angle is 72. What is the length of each leg? 23. It is often helpful to know the trigonometric ratios form 30, 45, 60 angles without using the calculator. Use the special triangle from the last unit to complete the following. Write as ratios, not decimals. sin cos tan 30 45 60 24. The diagonal of a rectangle is 10. The length is 2 more than the width and perimeter is 28. Find the measure of the two angles of different sizes formed by a side and a diagonal. 25. The length of the altitude to the base of an isosceles triangle is 12cm. The angle not congruent to the other two has measure 72. Find the length of one of the congruent sides. 26. An airplane that climbs at a steady rate to reach an altitude of 30,000ft covers 32 mile of ground distance. Find the measure of the angle of the climb. 27. A person 1000ft from the base of the Washington Monument finds the angle the ground makes with the line of sight to the top of the monument to be about 29. About how high is the monument? 28. An 18ft ladder leans against a house that stands on level ground. The foot of the ladder is 10ft from the house. Find the measure of the angle that the foot of the ladder makes with the ground. 29. If the 622-ft tall Tower of the Americas in San Antonio casts 260-ft shadow. What is the angle of elevation of the sun to the nearest degree? 30. An observer at the top of a 50m lighthouse (with its base at sea level) sees tow boats approaching, one behind the other. The angles to the boats are 39 and 25. Find the distance between the boats. 31. From a point 340m from the base of the Hoover Dam, the angle of elevation to the top of the dam is 33. Find the height of the dam.
32. A county ordinance specifies that a wheelchair ramp can rise a maximum of one foot for each fifteen feet of horizontal run. What is the maximum permissible angle of the ramp? 33. From a lighthouse 1000ft above sea level, the angle of depression to a boat at B is 29. One minute later, the boat is a point A and angle of depression measures 44. How far has the boat traveled? What is its speed in feet per hour? 34. The pilot of a helicopter at an altitude of 10,000ft sees a second helicopter at an angle of depression of 30. The altitude of the second helicopter is 8000ft. What is the distance from the first to the second along the line of sight? What is the horizontal distance between them? Find both answers to the nearest hundred feet. 35. A helicopter pilot sights a life raft. His angle of depression is 28, and the helicopter s altitude is 2.5km. What is the horizontal distance from the helicopter to the raft? If the helicopter flies at a constant speed of 200km/hr, how long will it be before it is directly above the raft? Assume that the altitude of the helicopter does not change. 36. A surveyor needs to find out how far away she is from a 3000-ft cliff. If her angel of elevation is 22, how far is she from the cliff? 37. The leaning tower of Pisa is 179ft tall (vertical). It makes an angle of approximately 85 with the ground. About how far over does the tower lean? 38. The included angle between the 10-m and 15-m sides of a triangular garden plot measures 31. Find the length of the altitude to the shorter side. 39. Only one of the three trigonometric ratios you have studied can have a value larger than 1. Identify the ratio, and explain why the values of the other two can never be greater than 1. 40. Sonar on a destroyer detects a submarine 400m away (horizontal). If the angle is 31, what is the depth of the submarine? 41. A car drives up a slope of 6 for 150m and drives another 100m at a slope of 9. How far has the car climbed vertically?
42. The angles of depression to the near and far banks of a river are 49 and 11, respectively. If the observer is 1.8m tall, how wide is the river? 43. A pilot at an altitude of 2000ft is over s spot 8020ft from the end of an airport s runway. At what angle of depression should the pilot see the end of the runway? 44. A ranger is at the top of a 200-ft lookout tower located on a flat plain. She spots a fire at an angle of depression of 3 from the top of her tower. How far away is the fire from the base of the tower? 45. A firefighter is rescuing a cat in a tree. If the branch that the cat is on is fifteen feet above the ground and the ladder makes an angle of sixty-three degrees with the ground, how long is the ladder? 46. A cable is used to support a 245-m television tower. If the angle the cable makes with the ground is 78, how long is the cable? 47. A person on a bridge sights a boat at an angle of depression of 6. The bridge is 96ft above the water. If the boat is traveling 440ft per minute, about how long will it take the boat to reach the bridge? 48. On a tour of Washington D.C., Martha goes to the top of the 555-ft tall Washington Monument. She sees her friend Chris 210ft from the base of the monument. Find the angle of depression. Also, find the line of sight. 49. An airplane rises vertically 1000ft over a horizontal distance of 1 mile. What is the angle of elevation of the airplane s path? 50. Richard is flying a kite. The kite string makes an angle of 57 with the ground. If Richard is standing 100ft from the point on the ground directly below the kite, find the length of the kite string. 51. If the length of each leg of an isosceles triangle is 24 and a base angle has measure 55. How long is the base?