### Instruction: Compute $\sin 30^\circ$.### Response: I know that $\sin 30^\circ$ is one of the special angles that can be found using a 30-60-90 triangle.
In such a triangle, the hypotenuse is twice the length of the shorter leg, and the longer leg is $\sqrt{3}$ times the shorter leg.
If I let the shorter leg be $x$, then the hypotenuse is $2x$ and the longer leg is $\sqrt{3}x$.
The angle opposite the shorter leg is $30^\circ$, so $\sin 30^\circ$ is the ratio of the opposite side to the hypotenuse.
Therefore, $\sin 30^\circ = \frac{x}{2x} = \frac{1}{2}$.