Question

On a straight line passing through the foot of a tower, two points C and D are at distance of 4cm and 16cm from the foot respectively. If the angles of elevation from C and D of the top of the tower are complementary, then find the height of the tower.

Answer 1

Hi friend,

Let the angles of elevation be x and y
given that   x+y=90
let the height of the tower = H

tan x =H/4
tan y =H/16
since x+y=90
tan(x+y)=infinite
(tanx + tany)/(1-tanx*tany)=infinite
1- tanx*tany= 0
1- (H^2)/64=0
[H^2=64
H=8] ANSWER

HOPE THIS HELPS YOU:-))