Question

How do I solve this?

Answer 1

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=√(a^2 + o^2) \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{y}\\ a=\stackrel{adjacent}{1}\\ o=\stackrel{opposite}{1} \end{cases} \\\\\\ y=√( 1^2 + 1^2)\implies y=√( 1 + 1 ) \implies y=√( 2 ) \\\\[-0.35em] ~\dotfill`

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=√(a^2 + o^2) \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{x}\\ a=\stackrel{adjacent}{√(2)}\\ o=\stackrel{opposite}{13} \end{cases} \\\\\\ x=\sqrt{ (√(2))^2 + 13^2}\implies x=√( 2 + 169 ) \implies x=√( 171 )\implies \boxed{x=3√(19)}`