Compute $\tan 45^\circ$.
I know that $\tan \theta$ is the ratio of the opposite side to the adjacent side in a right triangle with angle $\theta$. I also know that a 45-45-90 right triangle has two congruent legs of length $s$ and a hypotenuse of length $s\sqrt{2}$. The opposite and adjacent sides are both $s$, so $\tan 45^\circ = \frac{s}{s} = 1$. 