To find the length of the missing leg (a) in a right triangle, you can use the Pythagorean theorem, which states that:
\[ a^2 + b^2 = c^2 \]
Where:
- \( a \) is the length of the missing leg,
- \( b \) is the length of one leg (17 inches),
- \( c \) is the length of the hypotenuse (15 inches).
However, it appears there might be a misunderstanding because in a right triangle, the hypotenuse is always the longest side. Here, \( c = 15 \) is less than \( b = 17 \). If 17 is one leg, then 15 cannot be the hypotenuse.
If you meant for \( b \) to be the hypotenuse, you can calculate \( a \) as follows:
\[ a^2 + 15^2 = 17^2 \]
Calculating the squares:
\[ a^2 + 225 = 289 \]
Now, isolate \( a^2 \):
\[ a^2 = 289 - 225 \] \[ a^2 = 64 \]
Now take the square root:
\[ a = \sqrt{64} = 8 \]
So, the length of the missing leg \( a \) is 8 inches.
Since the problem asks to round to the nearest ten, you would round 8 inches to 10 inches.