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OAB is a triangle in the horizontal pla...

` OAB ` is a triangle in the horizontal plane through the foot ` P ` of the tower at the middle point of the side ` OB ` of the triangle. If ` OA = 2m, OB = 6 m, AB = 5 m and /_AOB ` is equal to the angle subtended by the tower at ` A,` then the height of the tower is

A

`sqrt((11xx39)/(25xx3))`

B

`sqrt((11xx39)/(25xx2))`

C

`sqrt((11xx25)/(39xx2))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
2

`In Delta AOB`
`cos theta =(4+6-25)/(2xx6)=15/24=5/8`
`rArr 5/8 =(13-h^(2)xx25//39)/(12)`
`rArr h^(2) = 11/2xx39/25`
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Knowledge Check

  • The angle of elevation of the top Q of a tower PQ at a point A on the horizontal plane through P the foot of the tower is alpha . At a point B on AQ at a vertical height of a, the angle of elevation of the middle point R of the tower PQ is beta , then the height of the tower is

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