Question

A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff. At a point on the plane 9 m away from the tower, the angle of elevation of the top and the bottom of the flag-staff are respectively 60° and 30°. Find the height of the flag-staff and height of the tower.

Answer 1

Let AB is a flag-staff and BC is tower. 

Let AB = x m and BC =h m. A point D which is 9 m away from the foot of tower C on the plane. 

The angle of elevation of the top and the bottom of the flag-staff are 60° and 30° respectively. 

Hence ∠ADC = 60° and ∠BDC = 30°

From right angled ∆BCD

Hence, height of tower = 3√3 m

Again from right angled ∆ACD,

tan 60° = AC/DC

⇒ √3 = (h + x)/9

⇒ h + x = 9√3

⇒ 3√3 + x = 9√3

⇒ x = 9√3 – 3√3

= 6√3 m

∴ Hence, height of flag-staff in 6√3 m.