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A man sitting at a height 20m on a tall tree on a small island

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A man sitting at a height 20m on a tall tree on a small island in the middle of river observes two poles directly opposite each other on the two banks of river & in a line with the foot of the tree. If the angles of depression of the feet of the poles from a point at which the man is respectively. Find the width of river.

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A man sitting at a height 20m on a tall tree on a small island in the middle of river observes two poles directly opposite each other on the two banks of river & in a line with the foot of the tree. If the angles of depression of the feet of the poles from a point at which the man is respectively. Find the width of river.

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Text solutionVerified

Let

BC

be the width of river. And

∡

of depression on either side of the river are

30^{0}

and

60^{0}

rube. It is given that

A C = 20 m

Let

BC = x C D = y ∠ A BC = 30^{0}, ∠ A BC = 30^{0}, ∠ A D C = 60^{0}

△ A BC, tan B = \frac{A C}{BC} = \frac{20}{x} = \frac{1}{3} \Rightarrow x = 203

△ A D C, tan 60^{0} = \frac{20}{y} = y = \frac{20 3}{3}

x + y = \frac{80}{3} m =

width of river

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Question Text	A man sitting at a height 20m on a tall tree on a small island in the middle of river observes two poles directly opposite each other on the two banks of river & in a line with the foot of the tree. If the angles of depression of the feet of the poles from a point at which the man is respectively. Find the width of river.
Answer Type	Text solution:1
Upvotes	150

Text solutionVerified

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