PQR is a triangular park with PQ=PR=200 m.
A T.V. tower stands at the mid-point of QR. If the angles of elevation of the top of the tower at P,Q and R are respectively 45∘,30∘ and 30∘, then the height of the tower (in m) is:
A
50√2
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B
50
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C
100
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D
100√3
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Solution
The correct option is C100 Let ST=h (height of tower)
From figure it is clear that
In △STP, we have tan45∘=STPT PT=ST=h
In △STQ, we have tan30∘=STQT ⇒QT=h√3
Now, in △PTQ, we have PT2+QT2=2002 ⇒4h2=2002 ∴h=100 m