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, which states:
\[ a^2 + b^2 = c^2 \]
where \( a \) and \( b \) are the lengths of the legs, and \( c \) is the length of the hypotenuse.
In this case, let:
- \( a = 10 \) cm (one leg)
- \( c = 50.5 \) cm (hypotenuse)
- \( b \) = length of the other leg
Using the Pythagorean theorem, we can rearrange the equation to find \( b \):
\[ b^2 = c^2 - a^2 \]
Now we'll substitute the given values:
\[ b^2 = (50.5)^2 - (10)^2 \]
Calculating each term:
\[ (50.5)^2 = 2550.25 \]
\[ (10)^2 = 100 \]
Now substitute these values back into the equation:
\[ b^2 = 2550.25 - 100 \]
\[ b^2 = 2450.25 \]
Now, take the square root of both sides to find \( b \):
\[ b = \sqrt{2450.25} \approx 49.5 \]
Thus, the length of the other leg is approximately \( 49.5 \) cm. Rounding to the nearest tenth, we find:
\[ \boxed{49.5} \text{ cm} \]