Mathematics
At a point on level ground, the angle of elevation of a vertical tower is found to be such that its tangent is . On walking 192 m towards the tower, the tangent of the angle is found to be . Find the height of the tower.
Heights & Distances
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Answer
Let the height of tower QR be h meters and the angle of elevation be θ1 and θ2 at points P and S respectively.
So,
From figure,
QR = h meters
PQ = PS + QS = (192 + QS) meters.
Considering right angled △PQR, we get
Considering right angled △SQR, we get
Putting value of QS from Eq 2 in Eq 1 we get,
Hence, the height of the tower is 180 meters.
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