To find the length of the missing leg \( b \) in a right triangle, we can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where:
- \( a \) is one leg,
- \( b \) is the missing leg,
- \( c \) is the hypotenuse.
Given:
- \( a = 10 \) inches,
- \( c = 6 \) inches.
However, it seems there might be an error in your provided values because the hypotenuse \( c \) should be the longest side of a right triangle. In any right triangle, \( c \) should be greater than \( a \).
If you meant \( c \) as a hypotenuse (which typically should be longer than the legs), then the given values do not create a valid right triangle.
If instead, the values are \( a = 6 \) inches (the shorter leg) and \( c = 10 \) inches (the hypotenuse), we can find \( b \) using the corrected values:
- Substitute the values into the Pythagorean theorem:
\[ 6^2 + b^2 = 10^2 \]
- Calculate the squares:
\[ 36 + b^2 = 100 \]
- Solve for \( b^2 \):
\[ b^2 = 100 - 36 \] \[ b^2 = 64 \]
- Take the square root of both sides:
\[ b = \sqrt{64} = 8 \text{ inches} \]
Thus, if we adjust for the correct positioning of \( a \) and \( c \), the length of the missing leg \( b \) would be 8 inches. If you need it rounded to the nearest ten, it would be 10 inches.
Please verify the values for clarity.