Question

Find the length of the third side. If necessary right i. Simplest radical form

Answer 1

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=√(c^2 - a^2) \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{2√(41)}\\ a=\stackrel{adjacent}{10}\\ o=opposite \end{cases} \\\\\\ o=\sqrt{ (2√(41))^2 - 10^2}\implies o=\sqrt{ (2^2)(√(41))^2 - 100 } \implies o=√( (4)(41)-100 ) \\\\\\ o=√(164-100)\implies o=√(64)\implies o=8`