Question

On a straight line passing through the foot of a tower two points C and D are at distances 4m and 16m 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

let AB be the tower and B be its foot
given BC=4,BC=16 and ACB+ADC =90
let ACD be X and ADC becomes 90-X
let AB be y
from fig tanX =Y/4.....1,
tan(90-X)=Y/16
cot X =Y/16
tanX=16/Y......2

from 1and 2 we get
Y/4=16/Y
y^2=64
y=8