To find the measure of the hypotenuse of a right triangle with legs measuring 7 cm and 15 cm, you can use the Pythagorean theorem, which states:
\[ c^2 = a^2 + b^2 \]
where \( c \) is the hypotenuse, and \( a \) and \( b \) are the lengths of the legs. In this case, let \( a = 7 \) cm and \( b = 15 \) cm.
Now, plug in the values:
\[ c^2 = 7^2 + 15^2 \] \[ c^2 = 49 + 225 \] \[ c^2 = 274 \]
Next, take the square root of both sides to find \( c \):
\[ c = \sqrt{274} \]
Calculating that gives:
\[ c \approx 16.5529 \]
Rounding to the nearest tenth, the measure of the hypotenuse is:
\[ \boxed{16.6} \text{ cm} \]