Question

The top of a banquet hall has an angle of elevation of 45° from the foot of a transmission tower and the angle of elevation of the topmost point of the tower from the foot of the banquet hall is 60°. If the tower is 60 m high, find the height of the banquet hall in decimals.

Answer 1

In the diagram, PQ represents the banquet hall and SR represents the transmission tower.

So, SR = 60 m, ∠SQR = 60° and ∠PRQ = 45°.

Now, in ΔSQR,

tan 60° = `(SR)/(QR)`

⇒ `sqrt(3) = 60/(QR)`

⇒ QR = `60/sqrt(3)`

= 34.64

Also, in ΔPQR,

tan 45° = `(PQ)/(QR)`

⇒ 1 = `(PQ)/(34.64)`

⇒ PQ = 34.64

As a result, the banquet hall's height is 34.64 m.