Question

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

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, the Pythagorean theorem states that \(a^{2}+b^{2}=c^{2}\), where \(a = 40\), \(b = 30\), and \(c\) is the hypotenuse. So we substitute the values: \(40^{2}+30^{2}=c^{2}\).

Step2: Calculate the squares

\(40^{2}=1600\) and \(30^{2}=900\). Then \(1600 + 900=c^{2}\), so \(2500=c^{2}\).

Step3: Find the square root

Take the square root of both sides: \(c=\sqrt{2500}\). Since \(\sqrt{2500} = 50\), we get \(c = 50\).

Answer:

50