Question

From a baloon vertically above a straight road, the angles of depression of two cars at an instant are found to be 45° and 60°.If the cars are 100m apart, find the height of the baloon.

Answer 1

as this is the required answer for this question

Answer 2

Let AB be the distance of the two cars. 
∴ab = 100 mtrs
Let x be the vertical distance of the balloon from the road and O be the vertical point of that balloon on the road.
Again let y be the distance from A to O.
The angle of depression from balloon to point A is 45° and that of to point B is 60°.
∴tan 45°=x/y
→1=x/y
→x=y   ... (1)
again, tan 60°=x/(100-y)
→√3=x/(100-y)
→x=√3(100-y)   ... (2)
Equating (1) and (2), we have
y=100√3-y
→2*y=100√3
∴ y=50√3=x