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The angle of elevation of the top of a ...

The angle of elevation of the top of a building from the foot of the tower is `30^o`and the angle of elevation of the top of the tower from the foot of the building is `60^o`. If the tower is 50 m high, find the height of the building.

Text Solution

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Let AB be a tower and CD be the builiding.
Here, height of tower AB = 50 m.
`angleABC=60^(@), angleDBC=30^(@)`
In `DeltaABC`,
`tan60^(@)=(AB)/(BC)rArrsqrt3=50/(BC)`
`rArr" "BC=50/sqrt3 …(1)`
In `DeltaBCD`,
`tan30^(@)=(CD)/(BC)rArr1/sqrt3=(CD)/(BC)`
`rArr CD=(BC)/sqrt3=50/(sqrt3xxsqrt3)=50/3`
`rArr CD=16.67 m`
`:. " Height of the building " = 16.67 m`
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