Question

From a point on a bridge across a river, the angles of depression of
the banks on opposite sides of the river are 30 and 45. respectively. If the bridge
is at a height of 3 m from the banks, find the width of the river.​

Answer 1

Step-by-step explanation:

ANSWER

The given information is drawn in the attached figure.

Given:

AB(=CD=EF)=4 m

∠FAE=30o

∠DAC=45o

From definition of tan of an angle θ,we know: tan(θ)=BasePerpendicular

Hence, tan(∠FAE)=FAFE

             tan(30o)=FA4

             31=FA4

             FA=43 m

Similarly, tan(∠DAC)=DACD

                tan(45o)=DA4

                1=DA4

                DA=4 m

Width of the river is: w=EC

                                   w=FD

                                   w=FA+AD

                                   w=43+4 m