From a point on a bridge across a river the angles of depression of the banks on opposite side of the river are 30° and 45° respectively. If bridge is at the height of 30m from the banks, find the width of the river.
Let A and B be the points on the bank n opposite sides f the river and BC be the width of the river.
BC = BD+DC ⇒ (m.
AD be the height of the bridge.
In ∆ADC
tan 45° =
1
---------(1)
In ∆ADB
tan 30° =
------------(2)
Width of the river = (
⇒ 30√3+30
⇒ 30(√3+1)m.