angle of elevation

Question

Erick sights the top of building and finds the angle of elevation to be 35 degree. He moves 100 feet closer and finds that the angle is now 40 degree. what is the height of the building?

Answer 1

If 'h' is the height of the building, and X is the distance, then h/x =  tan 35 

therefore, x/h= 1/tan35     .....(1)

When he moves  100 feet toward the building the angle changes to 40⁰

so h/x-100 = tan 40

therefore ( x-100) /h = 1/tan 40

So x/h-100/h = 1/tan40 ....(2)

Subtracting (2) from (1) we get 100/h = 1/tan35-1/tan40 

therefore, h =  100 (tan40. tan35) /(tan 40- tan35)