PQR is 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:
A
50√2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
100
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
50
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
100√3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is B100 Let ST=h (height of tower)
From figure it is clear that PT=ST=h
In △STQ, we have tan30∘=STQT ⇒QT=h√3
Now, in △PTQ, we have PT2+QT2=2002 ⇒4h2=2002 ∴h=100 m