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
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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
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