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

Step-by-step solution

Let the height of the tower M N be h In ∆ Q M N tan 30 ° = M N Q M ∴ Q M = 3   h = M R    … ( 1 ) ∵ M is the point Q M = M R Now in Δ M N P ∵ ∠ M P N = ∠ N M P = 45 ° ∴ M N = P M ( ∵ In a triangle sides opposite to equal angles are equal . . . 2 ) ∴ M N = P M = h In ∆ P M Q By using Equation 1 P M = ( 200 ) 2 - ( 3   h ) 2    By using Pythagoras theorem ∴ From 2 h = ( 200 ) 2 - ( 3 h ) 2 ⇒ h =