Question

A 100-foot vertical antenna is on the roof of a building. From a point on the ground, the angle of elevation to the top and the bottom of the antenna are 51 degrees and 37 degrees, respectively. Find the height of the building to the nearest foot.
How would you solve for these?

Answer 1

if the point is x feet from the building, then if the building's height is h,

h/x = tan37°
(h+100)/x = tan51°

equating the values for x,

h/tan37° = (h+100)/tan51°
h = 156.55