A vertical antenna is mounted atop a 49 foot pole From a poi

A vertical antenna is mounted atop a 49 foot pole. From a point on level ground 74 feet from the base of the pole, the antenna subtends an angle of 20.2 degree find the length of the antenna. The length of the antenna is about feet. (Round to the nearest foot as needed.)

Solution

Let:
a = angle subtended by the 49 ft pole.
h = height of the antenna

tan(a) = 49/74
a = arctan(49/74)
a = arctan(0.662162162)
a = 33.51 degrees

tan(a+10.2) = (49+h)/74
tan(33.51+10.2) = (49+h)/74
tan(33.51+10.2) * 74 = (49+h)
(tan(33.51+10.2) * 74) - 49 = h
(0.95595473 * 74) - 49 = h
70.74065008 - 49 = h
21.74 = h
therefore height of antenna is 21.74 feet