A stationary balloon is observed from three points A ,   B and C on the plane ground and is found that its angle of elevation from each point is 60 o . If ∠ A B C = 3 0 o and A C = 5 meters, then the height of the balloon from the ground is

Step-by-step solution

Let, P Q be vertical with height h meters and at its end Q there is a balloon and P is on the ground ⇒ P A = P B = P C = h cot ⁡ 60 o = h 3 ∴ P is the circumcentre of Δ A B C and its circumradius R = h 3 In Δ A B C , 2 R = 5 sin ⁡ 30 o ⇒ 2 h 3 = 5 sin ⁡ 3 0 o ∴ h = 5 3 meters.