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प्रश्न
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.
उत्तर
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`
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