PQR is a triangular park with PQ = PR = 200m. 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:

Engineering

Mathematics

problems on height and distance

Question

100

$100 \sqrt{3}$

$50 \sqrt{2}$

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Let height of tower be h

$∴$ QM = h cot 30° = $\sqrt{3}$ h

and PM = h cot 45° = h

$∴$ PQ² = PM² + QM²

(200)² = 3h² + h²

h = 100 m.