question_answer

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 \[45{}^\circ \] and \[60{}^\circ \] respectively. Find the width of the river. [Use\[\sqrt{3}=1.732\]]

Answer:

Let aeroplane is at A, 300 m high from a river. C and D are opposite banks of river.

In right \[\Delta \,ABC\],

\[\frac{BC}{AB}=\cot \,\,60{}^\circ \]

\[\Rightarrow \]               \[\frac{x}{300}=\frac{1}{\sqrt{3}}\Rightarrow x=\frac{300}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}\]

\[=100\sqrt{3}m\]

\[=100\times 1.732=173.2\,m\]

In right \[\Delta \,ABD\],

\[\Rightarrow \]               \[\frac{BD}{AB}=\cot \,\,45{}^\circ \]

\[\Rightarrow \]               \[\frac{y}{300}=1\,\Rightarrow y=300\]

Width if river \[=x+y\]

\[=173.2+300\]

\[=473.2m\]