Q .From a point on a bridge across the river the angle of depression of the banks on opposite sides of the river are 45° and 30° respectively.
if the bridge is at the height of 4 from the banks. Find the width of the river (take √3 = 1.732 )

Height of bridge from the banks CD = 4m
∠CAD = 45°
∠CBD = 30°
so we have to calculate width of the river AB =?

So in △ACD according to basic concept-


AB : BC : CA = 1 : 1 : √2

CD = 1 part = 4m = AC

AC = 4

So in △BCD according to basic concept-



AB : BC : CA = 1 : √3 : 2

CD = 1 part = 4m;

AC = √3 part = 4m * √3

AC = 4 √3 m = ED

AC = 6.92

So width of the river BC = AC + BC
BC = 4 + 6.92
BC = 10.92