The image shows a right-angled triangle with vertices labeled A, B, and R. The right angle is at point A. The length of side AR is given as 8 units, and the length of side AB is given as 15 units. The length of the hypotenuse (side BR) is represented as $X$, which we need to calculate.

To find $X$, we can apply the Pythagorean Theorem, which states:

$a^2 + b^2 = c^2$

where $a$ and $b$ are the lengths of the two legs of the right-angled triangle (AR and AB), and $c$ is the length of the hypotenuse (BR).

Substituting the values: $8^2 + 15^2 = X^2$ $64 + 225 = X^2$ $289 = X^2$ $X = \sqrt{289} = 17$

Thus, the length of the hypotenuse $X$ is 17 units.

Would you like more details on the steps or have any further questions?

Here are some additional related questions:

1. How do we apply the Pythagorean Theorem to non-right-angled triangles?
2. Can the Pythagorean Theorem be used to find the area of a triangle?
3. What is the relationship between the angles of a right triangle and the sides?
4. How can we use trigonometry to solve right-angled triangles?
5. What other methods can be used to calculate the length of the hypotenuse?

Tip: When solving for missing sides of right-angled triangles, remember to always double-check if it is a right triangle and apply the Pythagorean Theorem correctly!