Question

The angle of elevation of the top of a tower from to points at distances of 4m and 9m from the base of the tower and in the same straight line with it are complementary. Show that the height of the tower is 6 meters.

Answer 1

Let AB be the tower and C and D be two points such that AC = 4m and AD = 9m.

Let:

AB = hm, ∠BCA = \(\theta\) and ∠BDA = 90° - \(\theta\)

In the right \(\triangle BCA,\) we have:

Height of a tower cannot be negative

∴ Height of the tower = 6 m