Let L be the length of the ladder, and consider the 75 degree angle. Thinking in terms of trig, the "opposite side" of the triangle formed by the ladder, the ground and the wall is 23 ft. Your job is to determine the length of the ladder, which is the same as the length of the hypotenuse of the triangle.
The sine function relates these two lenths:
opp. side 23 ft
sin 75 deg = ---------------- = --------------
hyp hyp
23 ft 23 ft
Solving for hyp, hyp = ---------------------- = ------------ = 23.8 ft sin 75 deg 0.956
The minimum ladder length would be 23.8 ft, which rounds up to 24 ft.
Check: is (23.8 ft)(sin 75) = 23 ft? Yes.
