Question

From the top of the tower  h metre high , the angles of depression of two objects , which are in the line with the foot of the tower are ∝ and ß (ß> ∝ ) cts . 

 

Answer 1

Let the two objects be at points C and D. 
The angle of depression for the point C is `ßß`  and for the point D is `∝∝` 
In ∆ABC, 

`tan ß=h/(BC)` 

`⇒ BC= h /tanß `

`⇒ tan∝= h/( BC+CD)` 

`⇒∝= h/(h/tanß+CD)` 

`⇒h/ tanß+CD= h/tan∝` 

`⇒ CD= h/tan∝-h/tanß`

`⇒ CD=h [1/tan∝-1/tanß]` 

`⇒CD=h [cot ∝-cot ß]`