This is a more complete solution to the ones mentioned above:
I think that a more straightforward way would be to use the sine here. As @zubzub mentioned, the side opposite a right angle is a hypotenuse (by definition). If we call the hypotenuse $h$, since sine = opposite/hypotenuse, $\sin 23º = 13/h$, so by rearrangement $(\sin 23º) (h) = 13$, or $h = 13/ \sin 23º$.
In future problems like this, keep 3 things in mind:
1) Make sure you know which units you are using. Degrees often have whole numbers and are much larger (from 0 to 360) than radians, which are often in multiples of $\pi$ (such as $5/3 \pi$).
2) Use the appropriate rule: the sine rule and cosine rule apply for non-right angled triangles, while for right angled triangles the basic trigonometric functions (sine, cosine, tangent and their inverses) are more practical, since they can be computed by definition.
3) Make sure to check your order of operations: $\sin(23/13)$ is a very different thing to $\sin(23)/13$! Check your calculator to see whether it follows the order of operations or not (most scientific calculators do), and add brackets in the right places when you are not sure whether to place them.