Question

A vertical pole and a vertical tower are on the same level ground in such a way that from the top of the pole, the angle of elevation of the top of the tower is 60^o and the angle of depression of the bottom of the tower is 30^o. Find: the height of the pole, if the height of the tower is 75 m. 

Answer 1

Let AB be the tower and CD be the pole. 

Then ∠ ACE = 60° and ∠ BCE = 30°

Let height of the pole be x m 

∴ CD=Be=x 

In Δ BEC, 

`(BE)/(EC)=tan 30° ` 

⇒ `EC=sqrt3 x` 

`In Δ  (AE)/(EC)=tan 60°` 

`⇒ (75-x)/(EC)= sqrt3` 

⇒ 75-x=3x

`∴ x=75/4=18.75 m`

∴ height of the pole is 18.75m.