(Q10) The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m, find the height of the tower from the base of the tower and in the same straight line with it are complementary.

Solution :

x90-x49h

Let the height of the tower = h m.

Angles of elevation of the top of the tower from two points = x° and (90° - x)

From the figure

tan x =
h
 ....(1)
Also tan(90o - x) =
h
cot x =
h
1
tan x
 =
h
∴ tan x =
h
 ....(2)

From (1) and (2)

tan x =
h
 =
h
∴
h
 =
h

h × h = ×

h2 =

∴ h = m