In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a=30 miles and b=72 miles, what is c? If necessary, round to the nearest tenth.

1 answer

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:

\[ \boxed{78.0} \text{ miles} \]