Question

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 degrees and B is 46 degrees , find the height of the tower.

Answer 1

As usual, draw a diagram.
A is farther away than B, so if B is x feet from the tower of height h,

h/x = tan46°
h/(x+80) = tan21°

or,

x = h cotn46° = h cot21° - 80
h = 80/(cot21°-cot46°) = 48.8 ft