### Instruction: Compute $\tan 60^\circ$.### Response: To find the value of $\tan 60^\circ$, I need to recall the definition of the tangent function as the ratio of the opposite side to the adjacent side in a right triangle.
I also need to recall a special right triangle that has a 60-degree angle, namely the 30-60-90 triangle.
In this triangle, the side opposite to the 60-degree angle is $\sqrt{3}$ times the length of the side adjacent to it, which is also the shorter leg of the triangle.
Therefore, $\tan 60^\circ$ is equal to $\frac{\sqrt{3}}{1}$, or simply $\sqrt{3}$.