Answer:
[tex]12\:\mathrm{ft}[/tex]
Step-by-step explanation:
When the ladder is leaning against the wall, a 30-60-90 triangle is formed. The ladder acts as a 24-foot hypotenuse. Because the height is facing the [tex]30^{\circ}[/tex] angle, the height is half the hypotenuse (30-60-90 rules). If you forget the side rules for a 30-60-90 triangle, simply use basic trig on the right triangle:
[tex]\sin 30^{\circ}=\frac{h}{24},\\h=24\sin 30^{\circ},\\h=24\cdot \frac{1}{2},\\h=\fbox{$12\:\mathrm{ft}$}[/tex].
