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A tower subtends an angle α at a point o...

A tower subtends an angle α at a point on the same level as the root of the tower and at a second point, b meters above the first, the angle of depression of the foot of the tower is β. The height of the tower is

A

b cot `alpha " tan " beta `

B

`b tan alpha tan beta `

C

`b tan alpha cot beta`

D

`b cot alpha cot beta`

Text Solution

Verified by Experts

Let AB be the tower of height h, D be the point x away fron B and C be another point b m above D

In triangle ABD.
`h=x tan alpha`
In triangle BCE. `X= b cot beta`
from (1) and (2) we get
`therefore h=b tan alpha cot beta`
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