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?

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