Question

The tower is 650 meters high. Suppose a building is erected such that the base of the building is on the same plane as the base of the​ tower, the angle of elevation from the top of the building to the top of the tower is 80.38° and the angle of depression from the top of the building to the foot of the tower is 65.05​°. How high would the building have to​ be?

Answer 1

`173.57\ m`

Explanation:

Let

h -----> the height of the building

x -----> the horizontal distance between the building and the tower

we know that

`tan(80.38\°)=(650-h)/x`

solve for x

`x=(650-h)/tan(80.38\°)` -----> equation A

`tan(65.05\°)=h/x`

solve for x

`x=h/tan(65.05\°)` ------> equation B

equate equation A and equation B and solve for h

`h/tan(65.05\°)=(650-h)/tan(80.38\°)`

`tan(80.38\°)h=(650-h)tan(65.05\°)`

`tan(80.38\°)h=(650)tan(65.05\°)-(h)tan(65.05\°)`

`h[tan(80.38\°)+tan(65.05\°)]=(650)tan(65.05\°)`

`h=(650)tan(65.05\°)/[tan(80.38\°)+tan(65.05\°)]`

`h=173.57\ m`