By the Pythagorean Theorem, the sum of the squares of the leg lengths aa and bb is equal to the square of the hypotenuse cc in a right triangle:

\(\displaystyle{a}^{{2}}+{b}^{{2}}={c}^{{2}}\)

Hence, \(\displaystyle{7}^{{2}}+{8}^{{2}}={c}^{{2}}\)

\(\displaystyle{49}+{64}={c}^{{2}}\)

\(\displaystyle{113}={c}^{{2}}\)

\(\displaystyle{c}=\sqrt{{113}}\sim{10.6}\)

\(\displaystyle{a}^{{2}}+{b}^{{2}}={c}^{{2}}\)

Hence, \(\displaystyle{7}^{{2}}+{8}^{{2}}={c}^{{2}}\)

\(\displaystyle{49}+{64}={c}^{{2}}\)

\(\displaystyle{113}={c}^{{2}}\)

\(\displaystyle{c}=\sqrt{{113}}\sim{10.6}\)