From a point P on the ground, the angle of elevation of the top of a 10 m tall building is 30o. A flagstaff is fixed at the top of the building and the angle of elevation of the top of the flagstaff from P is 45o. Find the length of the flagstaff and the distance of the building from the point P? [Take √3 = 1.73]
Let QR = 10 m be the building and RS be the flagstaff.
In Δ PQR,
tan 30° = QR/PQ
⇒ 1/√3 = 10/PQ
∴ PQ = 10√3 m = 10× 1.73 = 17.3 m
In Δ PQS,
tan 45° = QS/PQ
⇒ 1 = QS/17.3
∴ QS = 17.3 m
Thus, Length of the flagstaff = RS = QS-QR = 17.3 – 10 = 7.3 m
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