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An aeroplane flying at a height of $300 m$ above the ground passes vertically above another plane at an instant when the angles of elevation of the two planes from the same point on ground are $60^{\circ}$ and $45^{\circ}$ respectively. What is the height of the lower plane above the ground in metres?

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100 \sqrt{3}

\frac{100}{\sqrt{3}}

50

150 (\sqrt{3 + 1}) .

answer is A.

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Detailed Solution

It is given that an aeroplane flying at a height of

300 m

above the ground passes vertically above another plane at an instant when the angles of elevation of the two planes from the same point on ground are

60^{\circ}

and

45^{\circ}

respectively.
Let

P

and

Q

be the positions of planes.
Let O be the point of observation.
Question Image

From

ΔOMP,

MP = 300 m

⇒

OM = MPcot 60^{0}

⇒

OM = 300 \times \frac{1}{\sqrt{3}} m

⇒ OM

= 100 \sqrt{3}

ΔOMQ,

MQ = OM

Height of the lower plane,
⇒

MQ = OM = 100 \sqrt{3} m

.
Hence, the correct option is 1.

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