P Q R is a triangular park with P Q = P R = 200   m . A TV tower stands at the mid-point of Q R . If the angles of elevation of the top of the tower from P , Q and R are 45 o , 30 o and 30 o respectively, then the height of the tower (in meters) is

Step-by-step solution

In the figure P Q R is triangular park with P Q = P R = 200 . TV tower of height h stands at midpoint M of Q R . In triangle T M R , M R = h cot 30 o In triangle T M P , P M = T M = h In triangle P M R , P R 2 = P M 2 + M R 2 ∴ 200 2 = h 2 + 3 h 2 ∴ h = 100   m