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A vertical tower stands on a declivity w...

A vertical tower stands on a declivity which isinclined at `15^@` to the horizon. From the foot of the tower a man ascends the declivity from 80 feet and then finds that the tower subtends an angle of `30^@`. The height of the tower is

A

`40(sqrt(6)+sqrt(2))`

B

`20(sqrt(6)-sqrt(2))`

C

`40(sqrt(6)-sqrt(2))`

D

`80(sqrt(6)-sqrt(2))`

Text Solution

Verified by Experts

Let BC be the declivity and BA be the tower .

Using sine rule in `DeltaABC`, we get
`(BC)/(sin75^@)=(AB)/(sin30^@)`
` rArr AB = (80sin30^@)/(sin75^@)`
` rArr AB = (40xx2sqrt2)/(sqrt3+1)= 40(sqrt6-sqrt2)`
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