A right triangle has a hypotenuse of length 15 and a leg of length 9 . What is the length of the other leg of the triangle?

Step 1 ：We are given a right triangle with a hypotenuse of length 15 and one leg of length 9. We are asked to find the length of the other leg.

Step 2 ：We can use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This can be written as: \(a² + b² = c²\), where \(c\) represents the length of the hypotenuse, and \(a\) and \(b\) represent the lengths of the other two sides.

Step 3 ：In this case, we know the length of the hypotenuse (\(c = 15\)) and the length of one leg (\(a = 9\)), and we want to find the length of the other leg (\(b\)). We can rearrange the Pythagorean theorem to solve for \(b\): \(b = \sqrt{c² - a²}\).

Step 4 ：Substituting the given values into the equation, we get \(b = \sqrt{15² - 9²}\).

Step 5 ：Solving the equation, we find that \(b = 12.0\).

Step 6 ：Final Answer: The length of the other leg of the triangle is \(\boxed{12}\).