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 represent the height of the church and point C represent the position of the person.

BC = 80m 

Angle of elevation = ∠ACB = 45° 

In right-angled ∆ABC,

tan 45° = AB/BC … [By definition] 

∴ 1 = AB/80

∴ AB = 80m 

∴ The height of the church is 80 m.