Question

A triangle has side lengths of a=8, b=15, and c=17. is it a right triangle? show work. please help and thank you

Answer 1

well, if it's a right-triangle, then the sum of the square of the smaller sides will equal the square of the longer one or hypotenuse, hmmm if that's so? let's check

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{17}\\ a=\stackrel{adjacent}{8}\\ o=\stackrel{opposite}{15} \end{cases} \\\\\\ (17)^2= (8)^2 + (15)^2\implies 289=64+225\implies 289=289 ~~ \textit{\LARGE \checkmark}`