To find the length of the hypotenuse \( c \) in a right triangle, we can use the Pythagorean theorem, which states:
\[ c^2 = a^2 + b^2 \]
In this case, we have \( a = 30 \) miles and \( b = 72 \) miles. Plugging these values into the equation gives:
\[ c^2 = 30^2 + 72^2 \]
Calculating the squares:
\[ 30^2 = 900 \] \[ 72^2 = 5184 \]
Now adding these two results:
\[ c^2 = 900 + 5184 = 6084 \]
Next, we take the square root to find \( c \):
\[ c = \sqrt{6084} \]
Calculating the square root:
\[ c \approx 78.0 \]
So, rounding to the nearest tenth, the length of the hypotenuse \( c \) is:
\[ \boxed{78.0} \text{ miles} \]