math 115a
posted by aris 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 degrees and B is 46 degrees , find the height of the tower.

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