### Applications involving right triangles

```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 65  
x
340
729.13 feet
Soh – Cah - Toa
65⁰
340 feet
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 75  
x
55
205.3 feet
75⁰
55 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.
2000 ft
37⁰
3 3 2 3 .2 8 ft.
37⁰
sin 37  
2000
x
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
Just pretend
we are on
the cliff is the boat?
the boat.
100 ft
53⁰20’
53⁰20’
tan 53  20 ' 
100
x
74.4 ft .
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’
800 ft
9 7 8 .6 ft.
54⁰50’
sin 54  50 ' 
800
x
6. When the sun is 20⁰ above the horizon, how
long is the shadow cast by a building 150 feet
high?
tan 20  
150
x
x
150
tan 20 
150 ft
x  4 1 2 .1 ft.
x
20⁰
7. A tree 100 feet tall casts a shadow 120 feet
long. Find the angle of elevation to the sun.
tan x 
100
150
100 ft
tan
1
 100 

 x
 150 
x  3 3 .7 
120 ft
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?
tan 40  
x
60
X = 50.3 feet
40⁰
60 feet
40 feet
40 feet
90.3 feet
```