Angle of Elevation? (30)?

Question

A 150-foot antenna is on top of a tall building. From a point on the ground, the angle of elevation to the top of the antenna is 28.5 degrees, while the angle of the elevation to the bottom of the antenna from the same point is 23.5 degrees. How tall is the building?

Answer 1

Height of building + antenna = b + 150. Angle to top is A. Distance from building is d. So (b+150)/d = tan A. Similarly, if angle to top of building is B, b/d = tan B.

Solving each equation for d, we have

(b+150)/tan A = d = b/tanB
(b + 150) tan B = b tan A
b tan B + 150 tan B = b tan A
150 tan B = b tan A - b tan B
150 tan B = b (tan A - tan B)
b = (150 tan 23.5°) / ( tan 28.5° - tan 23.5°)
b = 603.1 ft.