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Question

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 $ 60°$. If the tower is $ 50 m$ high, find the height of the building.


50m

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Solution

From the given figure,

Step 1- Finding the value of base BC

the height of the tower CD=50m

InBCDtan60°=CDBC3=50BCBC=503m-------(eq1)

Step 2- Finding the height of building AB

InABCtan30°=ABBC13=AB503(fromeq1)AB=13×503mAB=503m

Hence, the height of the building is AB=503m


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