#### Question

The angles of elevation and depression of the top and the bottom of a tower from the top of a building, 60 m high, are 30° and 60° respectively. Find the difference between the heights of the building and the tower and the distance between them.

#### Solution

Let AB be the building and CD be the tower.

In right ∆ABD:

`(AB)/(BD)=tan 60^@`

`⇒ 60/(BD)=sqrt3`

`⇒ BD=60/sqrt3`

`⇒ BD=20sqrt3`

In right ∆ACE:

`(CE)/(AE)=tan 30^@`

`⇒ (CE)/(BD)=1/sqrt3 (∵AE=BD)`

`⇒CE=(20sqrt3)/sqrt3=20`

Height of the tower = CE + ED = CE + AB = 20 m + 60 m = 80 m

Difference between the heights of the tower and the building = 80 m − 60 m = 20 m

Distance between the tower and the building = BD = `20sqrt3`

Is there an error in this question or solution?

Solution The angles of elevation and depression of the top and the bottom of a tower from the top of a building, 60 m high, are 30° and 60° respectively. Find the difference between the heights of the building and the tower and the distance between them. Concept: Heights and Distances.