1. For a person standing at a distance of 80 m from a church, the angle of elevation of its top is of measure 45º. Find the height of the church.

1. For a person standing at a distance of 80 m from a church, the angle of elevation of its top is of measure 45º. Find the height of the church.

Solution:

Let, seg AB represents the church C represents the position of observer.

BC = 80 m

∠ ACB is the angle of elevation

m ∠ ACB = 45º

In right angled ∆ ABC,

tan45⁰ = AB/BC  [By Definition]

∴ 1 = AB/80

∴  AB = 80 m

∴ The height of the church is 80m.