question_answer

An aeroplane flying at a height of 300 m above the ground phase vertically above another plane at an instant when the angle of elevation of the two planes from the same point on the ground are\[60{}^\circ \]and \[45{}^\circ ,\]respectively. The height of the lower plane from the ground (in metre) is     

A)        \[100\sqrt{3}\]

B)  50        

C)  \[\frac{100}{\sqrt{3}}\]

D)  150      

Correct Answer: A

Solution :

Let Q and R be the position of two planes.

Here      \[OQ=300\,\,m\]

In \[\Delta POR,\]

We have,           \[OP=OR\]

Now, in \[\Delta POQ,\]

\[\tan 60{}^\circ =\frac{OQ}{OP}=\frac{300}{OR}\]     \[(\because OP=OR)\]

\[\sqrt{3}=\frac{300}{OR}\]\[\Rightarrow \]\[OR=\frac{300}{\sqrt{3}}=100\sqrt{3}\,\,\text{m}\]