Question

From an aeroplane vertically above a straight horizontal road, the angles of depression of two consecutive mile stones on opposite sides of the aeroplane are observed to be α and β. Show that the height in miles of aeroplane above the road is given by

$\frac{\tan \alpha \tan \beta }{\tan \alpha +\tan \beta }$

Answer 1

Let be the height of aero plane above the road. And and be the two consecutive milestone, thenmile. We have and.

We have to prove that

The corresponding figure is as follows

In

Again in

Now,

Hence height of aero plane is