A tower is on a horizontal plane. The angles of elevation of top of the tower from two points on a line passing through the foot of the tower at distances 49m and 36m are 41∘ m and 49∘. The height of the tower is :
42 m
Let h be the height of the tower.
In Δ ABC, tan 49∘=h36 …(1)
In Δ ABD, tan 41∘=h49⇒ cot(90∘−41∘)=h49
⇒ cot 49∘=h49 …(2)
Multiplying (1) and (2), we get tan 49∘ cot 49∘=h236×49
⇒ h2=36×49⇒h=6×7=42 m