Question

An aeroplane is flying at a height of 300 m above the gound. Flying at this height the angles of depression from the aeroplane of two points on both banks of a river in opposite directions are ${45}^{\circ }$ and ${60}^{\circ }$ respectively. Find the width of the river. [Use~$\sqrt{3}=\mathrm{1.732.}$]

Answer 1

Let A be the position of the aeroplane such that AD = 300 m

Let B and C be the points of observation on the 2 banks of the river.

Let BC be the width of the river.

Let $\angle ABD={60}^{\circ }$ and $\angle ACD={45}^{\circ }$
In $△ABD$




In $△ADC$




⇒DC = 300 m

Now, BC = BD + DC = 100 + 300 = 100×1.732 + 300 = 173.2 + 300 = 473.2 m

Width of the river = 473.2 m