so the triangle has 3 sides, keeping in mind that the longest side is always the hypotenuse "c".
so the sides' lengths are 8, 10 and 15, so the legs are 8 and 10, the hypotenuse is 15 hmmmm, well, from the pythagorean theorem, c² = a² + b², meaning the square of the hypotenuse has to equal the sum of the square of the other two, let's see if that's true.
[tex]\bf \textit{using the pythagorean theorem}
\\\\
c^2=a^2+b^2\implies c=\sqrt{a^2+b^2}
\qquad
\begin{cases}
c=hypotenuse\\
a=\stackrel{adjacent}{8}\\
b=\stackrel{opposite}{10}\\
\end{cases}
\\\\\\
c=\sqrt{8^2+10^2}\implies c=\sqrt{64+100}\implies c=\sqrt{164}
\\\\\\
c\approx 12.81\qquad \qquad \stackrel{\textit{nope, no dice, is not a right-triangle}}{c\ne 15}[/tex]
