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**Applications Involving Right Triangles**

Soh – Cah - Toa

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1. From a point 340 feet away from the base of the Peachtree Center Plaza in Atlanta the angle of elevation to the top of the building is 65⁰. Find the height of the building. 65⁰ 340 feet Soh – Cah - Toa

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2. A guy wire from the top of a transmission tower at radio station WJBC forms a 75⁰ with the ground at a 55 foot distance from the base of the tower. How tall is the tower? 75⁰ 55 feet

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**3. An airplane sights a spotlight on the ground at the airport**

3. An airplane sights a spotlight on the ground at the airport. If the angle of depression to the light is 37⁰ and the airplane’s altitude is 2000 feet, how far away is the spotlight along the line of sight? That’s right it’s a G6. 37⁰ X = line of sight 2000 ft 37⁰

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**Just pretend we are on the boat.**

4. From a point on the edge of a cliff 100 feet above a lake the angle of depression to a boat on the lake is 53⁰20’. How far from the base of the cliff is the boat? Just pretend we are on the boat. 53⁰20’ 100 ft 53⁰20’

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5. A pilot returning to an aircraft carrier is 800 feet above the water. When he finds that the angle of depression to the carrier is 54⁰50’. How far away is the carrier along the flight path? 54⁰50’ X = Flight path 800 ft 54⁰50’

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**6. When the sun is 20⁰ above the horizon, how long is the shadow cast by a building 150 feet high?**

150 ft x 20⁰

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**7. A tree 100 feet tall casts a shadow 120 feet long**

7. A tree 100 feet tall casts a shadow 120 feet long. Find the angle of elevation to the sun. 100 ft 120 ft

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**8. Two buildings with flat roofs are 60 feet apart**

8. Two buildings with flat roofs are 60 feet apart. From the roof of the shorter building, 40 feet in height, the angle of elevation to the edge of the roof of the taller building is 40⁰. How high is the taller building? X = 50.3 feet 40⁰ 60 feet 40 feet 40 feet 90.3 feet

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