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
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