An aeroplane flying at a height of 300 metres 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 the ground are 60° and 45°, respectively. Then the height of the lower plane from the ground, in metres, is

As per the given question,

Let, the height of first plane be 'AC' which is equal to 300m. Height of second plane be 'BC'.

From triangle ACD,

tan 60$$^{\circ} = \frac{300}{CD}$$

$$\sqrt{3} = \frac{300}{CD}$$

CD = $$\frac{300}{\sqrt{3}}$$......(1)

From triangle BCD,

tan 45$$^{\circ} = \frac{BC}{CD}$$

CD = BC ...........(2)

From equations (1) and (2) 

BC = $$\frac{300}{\sqrt{3}}$$

BC = 100$$\sqrt{3}$$

Hence, option A is the correct answer.