Question

A painter is placing a ladder to reach the third story window, which is 12 feet above the ground and makes an angle of 80 degrees.how far out from the building does the base of the ladder need to be positioned

Answer 1

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

in this problem
see the attached figure to better understand the problem
angle ∅=80°
opposite side angle ∅=12 ft (AB)
adjacent side angle ∅=? (AC)
adjacent side angle ∅=12/tan 80°------> 2.12 ft

the answer is
2.12 ft