From the top of a building 15 m high the angle of elevation of the top of a tower is found to be 30°. From the bottom of the same building, the angle of elevation of the top of the tower is found to be 60°. Find the height of the tower and the distance between the tower and building.

Question

From the top of a building 15 m high the angle of elevation of the top of a tower is found to be 30&#xB0;. From the bottom of the same building, the angle of elevation of the top of the tower is found to be 60&#xB0;. Find the height of the tower and the distance between the tower and building.

Philoid · Accepted Answer

Let the distance between tower and building = (m)

In ∆ABC,

tan 60° =

√3 =

=

√3 = h+15

h = √3-15 ------(1)

In ∆ABE,

tan 30° =

---------(2)

h = 3h-15 ⇒ 2h = 15

h = ⇒ 7.5 m.

Height of tower = 15+7.5 ⇒ 22.5 m.

⇒ 12.99 m.

Therefore distance between tower and building is 12.99 m.