Question

The angle of elevation of the top of a tower standing on a horizontal plane from a point C is α. After walking a distance d towards the foot of the tower the angle of elevation is found to be β. The height of the tower is

A. \(\frac{d}{cot\,a+cot\,β}\)

B. \(\frac{d}{cot\,a-cot\,β}\)

C. \(\frac{d}{tan\,β-tan\,a}\)

D.\(\frac{d}{tan\,β+tan\,a}\)

Answer 1

Given: 

The angle of elevation of the top of a tower standing on a horizontal plane from a point C is α. After walking a distance d towards the foot of the tower the angle of elevation is found to be β. 

To find: 

The height of the tower 

Solution:

Let h be the height of the tower on horizontal plane. 

Let α be the angle of elevation from point C and β be the angle of elevation from point B 

Given CB = d 

In Δ PCB

⇒ tanβ ( h - d tanα) = h tanα 

⇒ h tanβ - d tan a tanβ = h tan a 

⇒ h (tanβ – tan a) = d tan a tanβ

Hence (b) is the answer.