Right Triangle Trig Applications

Right Triangle Trig Applications WS 2 HPC Name:____________________________________ Hour:_______ 1. Find the measures of the acute angles of a right triangle whose legs are 9 cm and 16 cm long. 29.4°, 60.6° 2. A lighthouse keeper observes that there is a 3° angle of depression between the horizontal and the line of sight to a ship. If the keeper is 19 m above the water, how far is the ship from shore? 362.5 m 3. A surveyor is standing 50 feet from the base of a large tree. The surveyor measures the angle of elevation to the top of the tree as 71.5°. How tall is the tree? What happens to the angle of elevation if the surveyor moves further away from the tree? 149.43 ft 4. The legs of an isosceles triangle are each 21 cm long and the angle between them has a measure of 52°. What is the length of the third side? 18.4 cm 5. Points 𝐴 and 𝐵 are on the same side of a tower and are 10 m apart. The angles of elevation of the top of a tower are 40° and 54° respectively. Find the tower’s height. 21.5 m 6. In traveling across flat land you notice a mountain directly in front of you. Its angle of elevation to the peak is 3.5°. After you drive 13 miles closer to the mountain, the angle of elevation is 9°. Approximate the height of the mountain. 1.30 miles 7. A 30-meter line is used to tether a helium filled balloon. Because of a breeze, the line makes an angle of approximately 75° with the ground. What is the height of the balloon? 28.98 m 8. A safety regulation states that the maximum angle of elevation for a rescue ladder is 72°. A fire department’s longest ladder is 110 feet. What is the maximum safe rescue height? 104.62 ft 9. At a point 325 feet from the base of a building, the angle of elevation to the bottom of a smokestack atop the building is 31°, and the angle of elevation to the top of the smokestack is 39°. Find the height of the smokestack. 67.88 ft 10. While traveling across flat land, you notice a mountain directly in front of you. The angle of elevation to the peak is 2.5°. After you drive 18 miles closer to the mountain, the angle of elevation is 10°. Approximate the height of the mountain. 1.04 miles 11. A woman is standing on a hill sees a flagpole that she knows is 60 feet tall. The angle of depression to the bottom of the pole is 16° and the angle of elevation to the top of the pole is 20°. Find the woman’s distance from the flagpole. 92.31 ft. 12. An escalator 152 feet in length rises to a platform and makes 30° angle with the ground. Find the height of the platform above the ground. 76 ft 13. The sonar of a navy cruiser detects a submarine that is 4000 feet from the cruiser. The angle between the water level and the submarine is 31.5° How deep is the submarine? 2089.99 ft 14. Callie and Cassidy are standing 100 feet apart on a straight path at a zoo. They both spot a beautiful parrot flying in the air between them. The angles of elevation from the girls to the bird are 54° and 40°, respectively. How high up is the parrot? 52.13 ft 15. A surveyor is 100 meters from the base of a dam. The angle of elevation to the top of the dam measures 26°. The surveyor’s eye-level is 1.73 meters above the ground. Find the height of the dam to the nearest tenth of a meter. 50.5 m 16. A water tower is located 325 feet from a building. From a window in the building, an observer notes that the angle of elevation to the top of the tower is 39° and that the angle of depression to the bottom of the tower is 25°. How tall is the tower? How high is the window? Tower: 414.73 ft, Window: 151.55 ft