Applications Involving Right

Triangles

Soh – Cah - Toa

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.

tan 65340

x

65⁰ 340 feet

729.13 feetSoh – Cah - Toa

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?

tan 7555

x

75⁰ 55 feet

205.3 feet

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.

2000sin 37

x

3323.28 ft.37⁰20

00 ft

37⁰

X = line of sight

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?

100tan 53 20 '

x 74.4 .ft

100

ft

53⁰20’

53⁰20’

Just pretend we are on the boat.

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’

54⁰50’

800

ft

X = Flight path

800sin 54 50 '

x

978.6 ft.

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

20⁰

150

ft

150tan 20

x

x

150

tan 20x

412.1 ft.x

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

100

ft

120 ft

100tan

150x

1 100tan

150x

33.7x

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?

40⁰

60 feet

tan 4060

x

X = 50.3 feet

40 feet 40 feet

90.3 feet