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 aeroplaneare found to be a and b. Show that the height of the aeroplane is( tanα.tanβ)/(tanα+tanβ)

Answer 1

 

In Fig. 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 a and b respectively. Let PC = h.

In right-angled triangle ACP, we have

Now in right-angled triangle PCB, we have