An Aeroplan is flying at a height of 300 m above the ground. Flying at this height, the angles of depression from the Aeroplan of two points on both banks of a river in opposite directions are 45^o and 60^o respectively.

Question

An Aeroplan is flying at a height of 300 m above the ground. Flying at this height, the angles of depression from the Aeroplan of two points on both banks of a river in opposite directions are 45^o and 60^o respectively.
Find the width of the river. [Use = 1.732]

Philoid · Accepted Answer

Let us consider the above problem, by the following diagram, where 'A' depicts the aero plane, 'C' and 'D' depict two ends of river.

Now,

Angle of depression from plane to 'C' = ∠XAC = 45°

∠XAC = ∠ ACD = 45° = θ₁(say) [Alternate angles]

Angle of depression from plane to 'D' = ∠YAD = 60°

∠YAD = ∠ ADC = 60° = θ₂(say) [Alternate angles]

AP = Height at which aero plane is flying = 300 m

Now, In ΔACP and ΔADP

⇒ CP = 300 m

⇒DP = 100√3 m

⇒DP = 100(1.732)

⇒DP = 173.2 m

Now, distance between two banks, CD = CP + DP

⇒ CD = 300 + 173.2 = 473.2 m