Answer:
Step-by-step explanation:
The 20-ft ladder is the hypotenuse here; the longer leg has length 16 ft, and the shorter leg can be represented by b (base).
Then, applying the Pythagorean Theorem,
20^2 = 16^2 + b^2, or
400 = 256 + b^2, or
144 = b^2.
Taking the square root of both sides, we get b = 12 ft.
The ratio of the base to the hypotenuse is the cosine of the triangle formed here. Thus,
cos Ф = adj / hyp = 12 ft / 20 ft = 0.6
The angle that the ladder makes with the horizontal base is then
Ф = arccos 0.6, or 0.927 radian, or 53.1 degrees.
