To find the length of the other leg of a right triangle when one leg and the hypotenuse are known, we can use the Pythagorean theorem. The theorem states that in a right triangle, the sum of the squares of the two legs equals the square of the hypotenuse. This can be expressed with the formula:
\[ a^2 + b^2 = c^2 \]
where:
- \( a \) and \( b \) are the lengths of the legs,
- \( c \) is the length of the hypotenuse.
In this case:
- One leg \( a = 8 \) inches,
- The hypotenuse \( c = 12 \) inches,
- We need to find the other leg \( b \).
Substituting the known values into the Pythagorean theorem:
\[ 8^2 + b^2 = 12^2 \]
Calculating the squares:
\[ 64 + b^2 = 144 \]
Next, we isolate \( b^2 \):
\[ b^2 = 144 - 64 \]
\[ b^2 = 80 \]
Now, we take the square root of both sides to find \( b \):
\[ b = \sqrt{80} \]
We can simplify \( \sqrt{80} \):
\[ \sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \times \sqrt{5} = 4\sqrt{5} \]
Now, we will calculate \( 4\sqrt{5} \). Approximating \( \sqrt{5} \) (which is about 2.236):
\[ b \approx 4 \times 2.236 \approx 8.944 \]
Rounding to the nearest tenth, we find:
\[ b \approx 8.9 \]
Thus, the length of the other leg is approximately 8.9 inches.