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Q)

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 $45^{\circ},\; 30^{\circ}$ and $30^{\circ}$, then the height of the tower (in m) is :


( A ) $50 \sqrt{2}$
( B ) $50$
( C ) $100 \sqrt{3}$
( D ) $100$

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A)
Let the mid point of QR be T and height of the tower be XT. First we have to find the height of the triangle PQR, PT which will come out to be 100m. Then apply tan45 in triangle PXT and find XT which will be equal to PT. Hence the height of the tower is 100m. Thus the answer is option D.
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