The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 45°. If the tower is 30 m high, find the height of the building.

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#### Solution

Let AB be the building and CD be the tower.

In ΔCDB,

`(CD)/(BD)=tan45^@`

`=>30/(BD)=1`

⇒BD=30 m

In ΔABD,

`(AB)/(BD)=tan30^@`

⇒AB=BD × `1/sqrt3`

`=>AB=30/sqrt3=10sqrt3m`

Therefore, the height of the building is `10sqrt3m`

Concept: Heights and Distances

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