PQRis a triangular park with PQ=PR=200 m. A T.V. tower stands at the mid-point of QR. 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

The correct option is C 100
Let the height of the tower MN be h
In ΔQMN
tan 30° = MN/QM
∴ QM = √3h = MR.. (1)
(∵ Mis the mid-point QM=MR)
Now in ΔMNP
∵∠MPN = ∠NMP = 45°
∴ MN = PM (∵In a triangle sides opposite to equal angles are equal ) .. (2)
∴ MN = PM = h
In ΔPMQ
By using Equation (1)
PM = √(200)² - (√3h)²
By using Pythagoras theorem
∴From (2) h = √(200)² - (√3h)²
→h² = (40000) - 3h²
By squaring both the sides
→4h² = 40000
→h² = 10000m
→h = 100m
Hence option C is correct.