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From the bottom of a pole of height h, t...

From the bottom of a pole of height h, the angle of elevation of the top of a tower is `alpha`. The pole subtends an angle `beta` at the top of the tower. find the height of the tower.

A

`(hcot (alpha - beta ))/(cot (alpha - beta )- cot alpha`

B

`(h tan (alpha- beta))/(tan(alpha- beta ) - tan alpha)`

C

`(cot (alpha- beta))/(cot (alpha - beta)-cot alpha)`

D

None of these

Text Solution

Verified by Experts

Let AB be the tower of height H and CD be the pole

In triangle ABC, d =`hcotalpha`
In triangle AED,d `=(H-h)cot (alpha - beta)`
`rArr Hcotalpha= (H-h) cot(alpha-beta)`
`therefore H=(h cot (alpha - beta))/(cot (alpha - beta )- cot alpha `
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