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Mathematics · 2022 · 3 marks
CBSE 2022 · Region 4 · Set 3 · Q7
An aeroplane at an altitude of 200 metres observes the angles of depression of opposite points on the two banks of a river to be 45° and 60°. Find…
An aeroplane at an altitude of $\displaystyle 200$ metres observes the angles of depression of opposite points on the two banks of a river to be $\displaystyle 45$° and $\displaystyle 60$°. Find the width of the river. (Use $\displaystyle \sqrt{3}=1.732$ )
Marking-scheme solution
\[y=\frac{200}{\sqrt{3}}=\frac{200 \sqrt{3}}{3}
\]
∴ Width of river \(\displaystyle =A B=x+y=200+\frac{200 \sqrt{3}}{3}\)
\[\begin{aligned}
& A B=200+\frac{200(1 \cdot 732)}{3} \\
& =200+\frac{346 \cdot 4}{3}=200+115 \cdot 46=315 \cdot 46 \mathrm{~m}
\end{aligned}
\]
∴ Width of river \(\displaystyle =315.46 \mathrm{~m}\)
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