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Question

# The angles of elevation of the top of a tower from two points A and B lying on the horizontal plane through the foot of the tower are respectively 450 and 300. If A and B are on the same side of the tower and AB=48metre, then the height of the tower is:

A
24(3+1) metre
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B
24 metre
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C
142 metre
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D
96 metre
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Solution

## The correct option is A 24(√3+1) metreLet QA=xmQB=AB+QA=(48+x)mIn ΔPQA,∠PQA=90°,∠PAQ=45°tan45°=PQQA=PQx∴PQ=xm→(1)InΔPQB,∠PQB=90°,∠PBQ=30°tan30°=PQQB=PQ(48+x)⇒PQ=(48+x)√3m→(2)From (1)&(2)x=(48+x)√3⇒x=48√3−1m∴heightoftower(PQ)=x=48√3−1=24(√3+1)mOption A is correct

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