To find the length of the hypotenuse in a right triangle with sides of lengths 8 and 15, you can use the Pythagorean theorem, which states:
\[ c^2 = a^2 + b^2 \]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two sides.
Plugging in the values:
\[ c^2 = 8^2 + 15^2 \] \[ c^2 = 64 + 225 \] \[ c^2 = 289 \]
Now, take the square root of both sides to find \(c\):
\[ c = \sqrt{289} = 17 \]
Therefore, the length of the hypotenuse is 17.