Question

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

Explanation:

Step1: Recall Pythagorean theorem

The Pythagorean theorem for a right - triangle is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs of the right - triangle. Here \(a = 2\) inches and \(b = 8\) inches.

Step2: Substitute values into the formula

Substitute \(a = 2\) and \(b = 8\) into \(a^{2}+b^{2}=c^{2}\), we get \(2^{2}+8^{2}=c^{2}\), which simplifies to \(4 + 64=c^{2}\), so \(c^{2}=68\).

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{68}\). Since \(\sqrt{68}=\sqrt{4\times17}=2\sqrt{17}\approx 8.2\) (rounded to the nearest tenth).

Answer:

8.2