right triangle trigonometry

Question

Joshua has a ladder that is 12 ft long. He will lean the ladder against a vertical wall. For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 75°. Is it possible for Joshua to lean the ladder against the wall so that the top of the ladder is at least 11.8 ft above the ground?

Answer 1

draw a right triangle with the ladder, the vertical wall, and the ground distance

sin=opposite/hypotenuse

sin75º=n/12

n=sin75º*12

n=0.965925826*12

n=11.59 feet at most

so the answer is no

Answer 2

make the appropriate diagram.

sin 75 = h/12.

solve for h.

if h ≥ 11.8, the answer is yes