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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.
Solution
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.
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