### Instruction: Compute $\cos 30^\circ$.### Response: To find the cosine of 30 degrees, I can use a special right triangle that has a 30-60-90 angle ratio.
Such a triangle has side lengths of 1, $\sqrt{3}$, and 2, where the hypotenuse is 2 and the opposite side to the 30-degree angle is 1.
The cosine of an angle is the ratio of the adjacent side to the hypotenuse, so in this case, $\cos 30^\circ$ is $\frac{\sqrt{3}}{2}$.
This is the exact value of the cosine of 30 degrees, but I can also approximate it using a calculator.
Using a calculator, I get $\cos 30^\circ \approx 0.866$.