It looks like you're referring to a right triangle where the sides are 5, 12, and 13, and you want to find the tangent of angle $\angle X$. Based on the Pythagorean triple (5, 12, 13), we know that this is a right triangle, and the tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side.

Let's assume that $\angle X$ is opposite the side of length 5, and the adjacent side to $\angle X$ is of length 12. The hypotenuse has length 13, which is consistent with the Pythagorean triple.

The formula for the tangent of an angle in a right triangle is:

$\tan(X) = \frac{\text{opposite}}{\text{adjacent}} = \frac{5}{12}$

So, the tangent of $\angle X$ is:

$\tan(X) = \frac{5}{12}$

This is already a simplified fraction.

Would you like more details about this process or the relationship between the sides of right triangles? Here's a list of 5 related questions:

1. How can you use the Pythagorean theorem to find missing side lengths in a right triangle?
2. What are the basic trigonometric ratios in right triangles?
3. How do you calculate the tangent if the sides are not part of a Pythagorean triple?
4. How can you find the angle using the inverse tangent function?
5. What is the relationship between the sine, cosine, and tangent functions in a right triangle?

Tip: In right triangles, recognizing common Pythagorean triples (like 3, 4, 5 and 5, 12, 13) can help quickly identify the ratios for sine, cosine, and tangent!