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From a point on a bridge across a river the angles of depressi

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From a point on a bridge across a river the angles of depression of the banks on opposite sides of the river are 30 $^{o}$ and 45 $^{o}$ respectively. If the bridge is at a height of 4 m from the banks, find the width of the river.

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From a point on a bridge across a river the angles of depression of the banks on opposite sides of the river are 30

^{o}

and 45

^{o}

respectively. If the bridge is at a height of 4 m from the banks, find the width of the river.

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Text solutionVerified

The given information is drawn in the attached figure.

Given:

A B (= C D = EF) = 4 m

∠ F A E = 3 0^{o}

∠ D A C = 4 5^{o}

From definition of tan of an angle

θ

,we know:

tan (θ) = \frac{Perpendicular}{Base}

Hence,

tan (∠ F A E) = \frac{FE}{F A}

tan (3 0^{o}) = \frac{4}{F A}

\frac{1}{3} = \frac{4}{F A}

F A = 43 m

Similarly,

tan (∠ D A C) = \frac{C D}{D A}

tan (4 5^{o}) = \frac{4}{D A}

1 = \frac{4}{D A}

D A = 4 m

Width of the river is:

w = EC

w = F D

w = F A + A D

w = 43 + 4 m

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Question Text	From a point on a bridge across a river the angles of depression of the banks on opposite sides of the river are 30 $^{o}$ and 45 $^{o}$ respectively. If the bridge is at a height of 4 m from the banks, find the width of the river.
Answer Type	Text solution:1
Upvotes	150