Question

An observer is 120 feet from the base of a television tower, which is 150 feet tall. find the angle of elevation of the top of the tower from the point where the observer is standing.

Answer 1

we know that
tan ∅=opposite side angle ∅/adjacent side angle ∅

in this problem
opposite side angle ∅=150 ft
adjacent side angle ∅=120 ft
∅=angle of elevation
so
tan ∅=150/120--------> 1.25
∅=arc tan(1.25)---------> ∅=51.34°

the answer is
51.34°