Question

what is the length of the hypotenuse? if necessary, round to the nearest tenth.
$c = \square$ miles

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, the Pythagorean theorem is \(a^2 + b^2 = c^2\), where \(a = 3\), \(b = 4\), and \(c\) is the hypotenuse. So we substitute the values: \(3^2 + 4^2 = c^2\).

Step2: Calculate the squares

\(3^2 = 9\) and \(4^2 = 16\), so \(9 + 16 = c^2\).

Step3: Sum the values

\(9 + 16 = 25\), so \(c^2 = 25\).

Step4: Take the square root

To find \(c\), we take the square root of both sides: \(c = \sqrt{25}\).

Step5: Simplify the square root

\(\sqrt{25} = 5\).

Answer:

5