college
posted by Ashley .
The angle of elevation from point A to the top of a vertical pole is 30.0 degrees. At point B, 6 meters closer to the base of the pole and on a line through the base of the pole and point A, the angle of elevation to the top of the pole is 37.0 degrees. Find the height ( to the nearest tenth of a foot) of the pole.

Let X be the distance from the closer point B) to the pole.
Let H be the height of the pole. You have two equations in two unknowns.
H/X = tan 37 = 0.75355
H/(X+6) = tan 30 = 0.57735
(X+6)/X = 1.3052 = 1 + 6/X
6/X = 0.3052
X = 19.66 m
H = 0.75355X = 14.8 m