Question

Please solve this question for me​

Answer 1

$\Large{\underline{\underline{\textbf{Question:}}}}$

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 the ground are 60° and 45° respectively. What is the height of the lower plane from the ground?

1. 500 m
2. 100/√3 m
3. 100√3 m
4. 150(√3 + 1) m

$\Large{\underline{\underline{\textbf{\green{Answer:}}}}}$

Let the ground distance between the point and the planes be x. The distance will be same for both the planes as they are vertical. The planes are at C and D.

AB = x

Let the height of lower plane be h.

BD = h

Given,

BC = 300

$\sf{tan 60° = 300/x}$

$\sf{tan 45° = h/x}$

$\sf{h = x = 300/tan 60°}$

h = 300/√3 = 100√3

The correct option is 3.