Question

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

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 40\) km and \(b = 30\) km, the Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse. So \(c^{2}=40^{2}+30^{2}\).

Step2: Calculate \(a^{2}\) and \(b^{2}\)

\(40^{2}=40\times40 = 1600\) and \(30^{2}=30\times30=900\). Then \(c^{2}=1600 + 900=2500\).

Step3: Solve for \(c\)

Take the square root of both sides. Since \(c>0\), \(c=\sqrt{2500}=50\) km.

Answer:

50