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PQR is triangular park with PQ=PR = 200 m. A tower stands at midpoint of QR, if elevation of top of tower at P, Q, R respectively are $45^{0}, 30^{0}, 30^{0}$ then height of the tower is

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100m

$100 \sqrt{3} m$

500m

$500 \sqrt{3} m$

answer is A.

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Detailed Solution

$T a n 30^{0} = \frac{h}{Q M} = \frac{h}{R M} \Rightarrow Q M = R M = \sqrt{3} h$

Now $∆$ PQM is a right angle triangle

$∴ Q M^{2} + P M^{2} = {(200)}^{2} \Rightarrow 3 h^{2} + h^{2} = {(200)}^{2} \Rightarrow h = 100$

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