To guard against a fall, a ladder should make and angle of 75* or less with the ground. What is the maximum height that a 20-foot ladder can reach safely?

The maximum height that a 20-foot ladder can reach safely is 17.32 feet. This can be calculated using the trigonometric equation: height = ladder length * cos(angle). In this case, height = 20 * cos(75) = 17.32 feet.

nope, that would be

h/20 = sin 75°
h = 20sin75 = 19.3 ft

btw, 20(cos75) would have been 5.18
I don't even see how you got your answer.