A man stands at a point …
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A man stands at a point X on the bank XY of a river with straight and parallel bank, and observes that the line joining X to a points Z on the opposite Bank makes an angle of 30° with XY. He then goes along the bank a distance of 200 metre to Y and find that the angle ZYX 60°. Find the breadth of the river.
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Rashmi Bajpayee 7 years, 1 month ago
Let the man 200 m to Y till point P.
Then, tan 30o = ZY / XY
1/√3 = ZY / (200 + PY)
ZY = (200 + PY)/√3. .........(i)
Again, tan 60o = ZY/PY
ZY = √3 PY .......(ii)
Equatind eq.(i) and (ii), we get,
(200 + PY)/√3 = √3 PY
200 + PY = 3PY
2PY = 200
PY = 100m
Therefore width of the river = XY = 200+ 100 = 300 m
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