To find the length of the other leg in a right triangle, we can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
Where:
- \( a \) and \( b \) are the lengths of the legs,
- \( c \) is the length of the hypotenuse.
In this case, one leg \( a = 12 \) in and the hypotenuse \( c = 16 \) in. We need to find the length of the other leg \( b \).
Substituting the known values into the theorem gives us:
\[ 12^2 + b^2 = 16^2 \]
Calculating the squares:
\[ 144 + b^2 = 256 \]
Now, subtract 144 from both sides:
\[ b^2 = 256 - 144 \] \[ b^2 = 112 \]
Next, take the square root of both sides to find \( b \):
\[ b = \sqrt{112} \] \[ b \approx 10.583 \]
Thus, the length of the other leg is approximately \( 10.6 \) in.
So, the answer is 10.6 in.
1 answer