JEE Main | 2018Height and DistanceHard

Question

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 45o, 30o and 30o, then the height of the tower (in m) is-

Options

A.

50

B.

1003

C.

502

D.

100

Solution


Let height of tower MN is 'h'
In ∆ QMN
MNQM = tan 30o
∴ QM = 3h  = MR    .....(1)
Now in ∆ MNP
MN = PM ......(2)
In ∆ PMQ
MP = (200)2-(3h)2
∴  From (2)
(200)2-(3h)2 = h ⇒h = 100 m

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