Question

III) From a point P on a bridge across a river, the angles of depression of the banks on the opposite side of the river are 30o and 45o respectively If the bridge is at a height of 3m from the banks, find the width of the river

Answer 1

Answer:

Step-by-step explanation:

Let the width of the river be AB

Angle of depression is 30° and 45°.

Therefor-:

∠ QPA = 30°    and      ∠RPB = 45°

Since PD is the height of the river, that means PD ⊥ AB.

Hence ∠PAD = 30°       and        ∠PBD = 45°

Tan A = PD/AD = Tan 30°

    AD =  3√3

Tan B = PD/BD = Tan 45°

    BD = 3

Hence the width of the river is = AD + BD = 3(√3 + 1) = AB