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 6 m from the banks, find the width of the river.
Open in App
The situation can be represented by the figure below. PQ is the bridge and BD is the river with B and D as two banks.
∠PAD=∠ADC and ∠QAB=∠ABC (Alternate angles)
tan ∠ADC=ACDC= tan 45∘⇒tan 45∘=6DC⇒DC=6mAlso, tan ∠ABC=ACBC \\