Question

From an aeroplane vertically above a straight horizontal plane, the angles of depression of two consecutive kilometre stones on the opposite sides of the aeroplane are found to be α and β . Show that the height of the aeroplane is (tanα.tanβ)/(tanα+tanβ).

Answer 1

In Fig. 11.57,let P be the position of plane, A and B be the positions of two stones one kilometre apart. Angles of depression of stones A and B are α and β respectively. Let PC = h.
In right-angled triangle ACP, we have