Question

The angles of the top of a tower from two points at a distance of 4 metre anf 9 metre from the base oof the tower and in the same straight line are complementary. Find the height of the towet?

Answer 1

6m

let the height of the tower=h m.

Angles of elevation of the top the tower from two points=x degrees and 90-x

Tan x=h/4.......(1)

Tan 90-x =h/9

Cot x=h/9 =1/tanx=h/9

Tanx =9/h ...............2

From 1 and 2

Tanx=h/9=9/h

h×h=9×4

h*2=36

h=

.

h=6m