Question

The angle of elevation of the top of a tower from certain  point on horizontal plane is 30° If the observer moves 20 m towards the tower, the angle of elevation of the top increases by 15°. Find the height of the tower.

Answer 1

Let AB is a tower of height h m. 

The angle of elevation of top of tower from point C is 30°. 

When moves 20 m towards the tower from point C, the angle of elevation increases 15°. 

i.e, ∠ACB = 30° and ∠ADB = 45°

From right angled ∆ABD,

tan 45° = AB/BD

⇒ l = h/BD

⇒ BD = h m …(i)

From right angled ∆ABC,

tan 30° = AB/BC

⇒ 1/√3 = h/(20 + BD)

Hence, height of tower = 10(√3 + 1)m.