A boy observes the top of a tower at 30°. After moving 40 m towards the tower, the angle becomes 60°. Find the distance, in metres, of the boy from the tower after moving.
Physics · Mathematical tools and vector · Trigonometric Function
NEET JEE Mains

Question

A boy observes the top of a tower at 30°. After moving 40 m towards the tower, the angle becomes 60°. Find the distance, in metres, of the boy from the tower after moving.

G1 Physics · Accepted Answer

Let the new distance be x and height h. From the nearer point, h=√3x. Initially the distance was x+40, so h=(x+40)/√3. Equate: 3x=x+40 ⇒ 2x=40 ⇒ x=20 m.