Question

Find the length of the third side. If necessary, write in simplest radical form.

Answer 1

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=√(c^2 - o^2) \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{10}\\ a=\stackrel{adjacent}{x}\\ o=\stackrel{opposite}{5} \end{cases} \\\\\\ x=√( 10^2 - 5^2)\implies x=√( 100 - 25 ) \implies x=√( 75 )\implies x=5√(3)`