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
`50 sqrt(2)`
B
100
C
50
D
`100sqrt(3)`
Text Solution
Verified by Experts
The correct Answer is:
B
In the figure PQR is triangle park with PQ=PR = 200 TV tower to height 'h' stands at midpoint M of QR In triangle TMR, `MR=h cot 30 ^@` In triangle TMP, PM=TM=h In triangle PMR, `PR^2= PM^2+MR^2` `therefore 200^2= h^2+3h ^2` `therefore h= 100m `
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