An aeroplane is flying at a height of 300 m above the ground

Trigonometry (10)

An aeroplane is flying at a height of 300 m above the ground. 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° and 60° respectively. Find the width of the river. [Use $\sqrt{3}$ = 1·732]

Answer

$$ \tan 45° = \frac{300}{y} $$

$$ 1 = \frac{300}{y} $$

$$ y = 300 $$

$$ \tan 60° =  \frac{300}{x} $$

$$ \sqrt{3} = \frac{300}{x} $$

$$ x = \frac{300}{\sqrt3} = \sqrt[100]{3} $$

$$ \text{Width of river} = 300 + \sqrt[100]{3} = 300 + 173.2 $$

$$ = 473.2 \; m $$

• Exam Year: 2017