To find the length of the missing leg \( a \) in a right triangle with legs \( b \) and \( c \), you can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
Here, \( b \) is one leg, \( c \) is the hypotenuse, and \( a \) is the other leg you want to find. Given your values:
- \( b = 20 \) inches
- \( c = 12 \) inches
Since \( c \) should be the hypotenuse, it should be the longest side. However, in this case, it seems like there is a mismatch because 20 > 12; thus it doesn't comply with the Pythagorean theorem.
Assuming you meant:
- \( a = 20 \) inches (the hypotenuse)
- \( b = 12 \) inches (one leg)
We can rearrange the Pythagorean theorem:
\[ a^2 = b^2 + c^2 \]
Let's recalculate it under the assumption that \( c \) is the missing leg:
\[ a = 20, \quad b = 12 \]
Then:
\[ 20^2 = 12^2 + c^2 \]
Calculating the squares:
\[ 400 = 144 + c^2 \]
Now, isolate \( c^2 \):
\[ c^2 = 400 - 144 \] \[ c^2 = 256 \]
Now, take the square root of both sides to find \( c \):
\[ c = \sqrt{256} = 16 \text{ inches} \]
Thus, the length of the missing leg \( c \) is \( 16 \) inches.