Answer:
In a right triangle, let's denote the sides as follows:
- \(AB\) represents the side opposite angle \(C\).
- \(BC\) represents the side adjacent to angle \(C\).
- \(AC\) represents the hypotenuse.
Using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (\(AC\)) is equal to the sum of the squares of the lengths of the other two sides:
\[AC^2 = AB^2 + BC^2\]
Given that \(AB = 15\) and \(BC = 8\), we can substitute these values into the equation:
\[AC^2 = 15^2 + 8^2\]
\[AC^2 = 225 + 64\]
\[AC^2 = 289\]
To find the length of \(AC\), we take the square root of both sides:
\[AC = \sqrt{289}\]
\[AC = 17\]
Therefore, the length of \(AC\) in the right triangle is \(17\) units.
Explanation: