An aeroplane flying at a height 300 metre 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

Options

A. 50m
B. `(100)/(sqrt(3))m`
C. `100sqrt(3)m`
D. `150(sqrt(3)+1)m`

Answer

C

Explanation

Let P and Q be the positions of two aeroplanes when Q is vertically below P and OP = 300 m
Let the angles of elevation of P and Q at a point A on the ground be `60^(@) and 45^(@)` respectively.
`:. ` In `DeltaAOQ`,
`tan 45^(@)=(OQ)/(OA)rArr OA = OQ`
In `Delta AOP`,
`tan 60^(@)=(OP)/(OA)=(300)/(OA)=sqrt(3)`
`rArr OA=(300)/(sqrt(3)=100sqrt(3)`
Hence, OQ`=100sqrt(3)`m