math
posted by Faw on .
two points A and B 80 ft. apart lie on the same side of a tower and in a horizontal line through its foot. if the angle of elevation of the top of the tower at A is 21 degree and B is 46 degree, find the height of the tower.

Let P be the foot of the tower, and h be the height of the tower
let AP = x , then BP = 80x
I see two rightangled triangles
tan21 = h/x > h = xtan21
tan46 = h/(80x) > h = (80x)tan46
xtan21 = (80x)tan46
xtan21 = 80tan46  xtan46
xtan21 + xtan46 = 80tan46
x(tan21 + tan46) = 80tan46
x = 80tan46/(tan21 + tan46)  I have not yet touched a calculator
you do the button pushing to get x
then plug x into
h = xtan21