To find the hypotenuse of a right triangle when the lengths of the two legs are given, we can use the Pythagorean theorem, which states:
\[ c^2 = a^2 + b^2 \]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the legs.
In this case, we have:
- \(a = 16 , \text{cm}\)
- \(b = 10 , \text{cm}\)
Now we can substitute the values into the formula:
\[ c^2 = 16^2 + 10^2 \]
Calculating the squares:
\[ c^2 = 256 + 100 \]
Now, adding these values together:
\[ c^2 = 356 \]
Next, we take the square root of both sides to find \(c\):
\[ c = \sqrt{356} \]
Calculating the square root:
\[ c \approx 18.9 , \text{cm} \quad (\text{rounded to the nearest tenth}) \]
Thus, the measure of the hypotenuse is approximately \( \boxed{18.9} , \text{cm} \).