To find the length of the missing leg \( b \) in a right triangle, you can use the Pythagorean theorem, which states that:
\[ a^2 + b^2 = c^2 \]
In this case, you are provided with:
- \( a = 17 \) (one leg of the triangle)
- \( c = 15 \) (the hypotenuse)
However, it seems there is a mistake in the values provided because, in any right triangle, the hypotenuse \( c \) must be the longest side. Since \( a \) is 17 and \( c \) is 15, it's not possible for \( c \) to be less than \( a \).
Please double-check the values of \( a \) and \( c \). If \( c \) is actually supposed to be more than 17, we can properly solve for \( b \) using the Pythagorean theorem.
Assuming you meant to have \( c = 17 \) and \( a = 15 \):
- Substitute the values into the formula:
\[ 15^2 + b^2 = 17^2 \]
- Calculate:
\[ 225 + b^2 = 289 \]
- Rearranging the equation gives:
\[ b^2 = 289 - 225 \]
\[ b^2 = 64 \]
- Take the square root of both sides:
\[ b = \sqrt{64} \]
\[ b = 8 \]
Thus, the length of the missing leg \( b \) is \( 8 \) inches.
If this isn't accurate due to a misunderstanding of the triangle's side lengths, please clarify.