From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower

Question

From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45&#xB0; and 60&#xB0; respectively. Find the height of the tower

Philoid · Accepted Answer

As per the question:

Let the height of building = p = 20 m

Therefore, total height of building and transmission tower = p’

The angle of elevation to the top of the building = 45° and that to the top of transmission tower = 60°

Height of transmission tower = ?

1^st case:

2^nd case:

Now, the height of the tower can be calculated as:

p'- p = 20√3 - 20

= 20(√3 - 1)

= 20(1.732 - 1)

= 20 × 0.732

= 14.64 m