Q. 724.2( 14 Votes )

An aeroplane is flying at a height of 210 m. Flying at this height at some instant the angles of depression of two points in a line in opposite directions on both the banks of the river are 45° and 60°. Find the width of the river.

Answer :

In the fig AD is the position of the aeroplane. Let the width of the river is DC = DB + BC


In ∆ABD



tan 45° =


1 =


x = 210m …………………(1)


In ∆ABC


tan 60° =


√3 =


√3y = 210


y =


On multiplying and dividing by √3, we get


y = = 70√3 ……………………(2)


Therefore width of the river is = 210 +70√3 = 331.24m


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