7.5 -7.7 Worksheet: Homework Name:________________ Trigonometry Applications Date:______ Period:____ Show all work. Express the lengths correct to the nearest unit and angle measures correct to the nearest degree. 1. A tree casts a shadow 21 m long. The angle of elevation of the sun is 51 . What is the height of the tree? 2. A helicopter is hovering over a landing pad 100 meters from where you are standing. The angle of elevation with the ground is 12 . What is the altitude of the helicopter? 3. You are flying a kite and have let out 80 meters of string. The angle of elevation with the ground is 40 . If the string is stretched straight, how high is the kite above the ground? 4. A guy (support) wire reaches from the top of a 120 meter television transmitter tower to the ground. The wire makes a 63 angle with the ground. Find the length of the guy wire. 5. From the top of a cliff at the edge of a lake, the angle of depression to a buoy on the lake is 33 . If the buoy is 80 meters from the base of the cliff, how high is the cliff? 6. A ship is 750 meters from a lighthouse, which is 50 meters tall. What is the angle of depression from the top of the lighthouse to the ship? 7. A tree 23 meters tall casts a shadow 17 meters long. Find the measure of elevation to the sun at that time? 8. A basketball hoop is 10 feet above the floor. What is the angle of elevation to the hoop from a point on the floor 15 feet from a point directly below the hoop? 9. Two television towers, each 100 meters tall, are 35 0 meters apart. Find the angle of elevation from the base of one tower to the top of the other. 10. A 15 meter pole is leaning against a wall. The foot of the pole is 10 meters from the wall. Find the measure of the angle the pole makes with the ground. 11. A reach stacker is a vehicle used to lift objects and move them between ships and land. a. The vehicle’s arm is 10.9 meters long. The maximum measure of A is 60 . What is the greatest height h the arm can reach if the vehicle is 3.6 meters tall? b. The vehicle’s arm can extend to be 16.4 meters long. What is the greatest height its extended arm can reach? 12. The triangle on the staircase below has a 52 angle and the distance along the stairs is 14 feet. a. What is the height h of the staircase? b. What is the length b of the base of the staircase?