Question

Adam and Kevin are standing 35 metres apart, on opposite sides of a flagpole. From Adam’s position, the angle of elevation of the top of the flagpole is 36°. From Kevin’s position, the angle of elevation is 50°. How high is the flagpole?

Answer 1

1. Lets' call:

H: The height of the flagpole.
x: The distance from Adam’s position to the flagpole.
y: The distance from Kevin’s position to the flagpole.

2. So, we have:

Tan(36°)=H/x ⇒ x=H/Tan(36°) (i)

Tan(50°)=H/y ⇒ y=H/Tan(50°) (ii)

3. We know that Adam and Kevin are standing 35 meters apart. Then:

x+y=35 (iii)

4. Let's substitute (i) and (ii) in (iii):

x+y=35
H/Tan(36°)+H/Tan(50°)=35
H(1/Tan(36°)+1/Tan(50°)=35

5. When we clear "H", we obtain:

H=35/(1/Tan(36°)+1/Tan(50°))
H=15.79 meters

How high is the flagpole?

The answer is: 15.79 meters