Q22 of 25 Page 9

From a point on a bridge across a river the angles of depression of the banks on opposite side of the river are 30° and 45° respectively. If bridge is at the height of 30m from the banks, find the width of the river.

To find: Width of the river.


Formula Used:



Explanation:


Let A and B be the points on the bank n opposite sides f the river and BC be the width of the river.



BC = BD+DC


= x + y


AD be the height of the bridge.


In ∆ADC




Y = 30 m ….. (1)


In ∆ADB




X = 30√ 3 ….. (2)


Width of the river = x + y


⇒ 30√3+30


⇒ 30(√3+1) m.


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