To find the length of the other leg of the right triangle, we can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where:
- \(a\) and \(b\) are the legs of the triangle, and
- \(c\) is the hypotenuse.
In this case, we know one leg \(a = 13\) cm and the hypotenuse \(c = 17\) cm. We need to find the other leg \(b\). We can rearrange the Pythagorean theorem to solve for \(b\):
\[ b^2 = c^2 - a^2 \]
Substituting the known values into the equation:
\[ b^2 = 17^2 - 13^2 \]
Calculating \(17^2\) and \(13^2\):
\[ 17^2 = 289 \]
\[ 13^2 = 169 \]
Now substituting these values back into the equation:
\[ b^2 = 289 - 169 \]
\[ b^2 = 120 \]
Now, take the square root of both sides to find \(b\):
\[ b = \sqrt{120} \]
Calculating the square root:
\[ b \approx 10.95 \]
Rounding to the nearest tenth gives:
\[ b \approx 11.0 \text{ cm} \]
Thus, the measure of the other leg is approximately 11.0 cm.