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

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 respectively `45^@` , `30^@` and `30^@` then the height of the tower in m is

A

100

B

50

C

`100 sqrt(3)`

D

`50 sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
A

Let height of tower TM be h.
In `DeltaPMT, tan 45^(@) = (TM)/(PM)`
`implies 1=(h)/(PM)`
implies PM=h
In `DeltaTQM, tan 30^(@) = (h)/(QM), QM=sqrt(3)h`
In `DeltaPMQ, PM^(2)+QM^(2)=PQ^(2)`
`h^(2)+(sqrt(3)h)^(2)=(200)^(2)`
`implies 4h^(2)=(200)^(2)`
`implies h = 100m`
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