Q. 314.3( 13 Votes )

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.

Answer :

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 (m.


AD be the height of the bridge.


In ∆ADC


tan 45° =


1


---------(1)


In ∆ADB


tan 30° =



------------(2)



Width of the river = (


30√3+30


30(√3+1)m.


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