From a point of the bridge of a river the angles of depression of the opposite banks of the river are 30° and 45°. If the bridge is at a height of 4m from the banks, then find the width of the river.

Let AB is the width of the river, Height between the river and the bridge is CF.

Given, ∠DCA = 30^o, ∠ECB = 45^o, CF = 4.

∠DCA = ∠CAB = 30^o

∠ABC = ∠ECB = 45^o

in ∆CAF

AF = CF√3 ……..(1)

in BCF,

FB = CF………..(2)

Width of the river = CF + CF

= 4(1 +