Question

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

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 3\) yd and \(b = 4\) yd, the Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse. So \(c^{2}=3^{2}+4^{2}\).

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

\(3^{2}=9\) and \(4^{2}=16\), then \(c^{2}=9 + 16\).

Step3: Find \(c^{2}\)

\(c^{2}=9+16=25\).

Step4: Solve for \(c\)

Take the square root of both sides. Since \(c>0\) (as it represents a length), \(c=\sqrt{25}=5\).

Answer:

5