The elevation of the top of a tower from a point on the ground is 45∘ . On travelling 60 m from the point towards the tower, the alevation of the top becomes 60∘ . The height of the tower, in metres, is

Explanation

From △ ACD, AD tan 60∘ = CD ⇒ AD = CD 3 From △ ABD, AD tan 45∘ = BD ⇒ AD = BD ⇒ AD = BC+CD AD (28) AD ⇒ AD = 60 + 3 AD ⇒ AD − 3 = 60 3 AD−AD ⇒ 3 = 60 AD( 3 − 1) = 60 3 60 3 AD = 3 −1 Rationalising above equation 60 3 3 +1 AD = 3 −1 × 3 +1 60 3 ( 3 +1) AD = 3 ∴ AD = 30( 3 + 3)