PQR is a triangular park with PQ = PR = 200m . A TV tower stands at...

PQR

is a triangular park with

PQ = PR = 200m

. A TV tower stands at the mid-point of

QR

. If the angles of elevation of the top of the tower from

P, Q

and

R

are

{45}^{o}

{30}^{o}

and

{30}^{o}

respectively, then the height of the tower (in meters) is PQR is a triangular park with PQ = PR = 200m . A TV tower stands at the mid-point of QR . If the angles of elevation of

PQR is a triangular park with PQ = PR = 200m . A TV tower stands at the mid-point of QR . If the angles of elevation of

Correct answer

100

Step-by-step solution

In the figure $PQR$ is triangular park with $PQ = PR = 200$ .

TV tower of height $h$ stands at midpoint $M$ of $QR$ .

PQR is a triangular park with PQ = PR = 200m . A TV tower stands at the mid-point of QR . If the angles of elevation of

In triangle $TMR$ , $MR = hcot{30}^{o}$

In triangle $TMP$ , $PM = TM = h$

In triangle $PMR$ , $P{R}^{2} = P{M}^{2} + M{R}^{2}$

$∴ {200}^{2} = {h}^{2} + 3{h}^{2}$

$∴ h = 100m$

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