Question

A person is standing at a distance of 80 m from a church looking at its top. The angle of elevation is of 45°. Find the height of the church.

Answer 1

Let AB be the church and C be the position of the person from the church.  

Suppose the height of the church be h m. 

In right ∆ABC,

\[\tan45^\circ = \frac{AB}{BC}\]

\[ \Rightarrow 1 = \frac{h}{80}\]

\[ \Rightarrow h = 80\] m

Thus, the height of the church is 80 m.