Question

Solve for x to the nearest tenth.

Answer 1

Check the picture below.

`\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}{7}\\ o=\stackrel{opposite}{8} \end{cases} \\\\\\ y=√( 7^2 + 8^2)\implies y=√( 49 + 64 ) \implies y=√( 113 ) \\\\[-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}{6}\\ o=\stackrel{opposite}{√(113)} \end{cases} \\\\\\ x=\sqrt{ 6^2 + (√(113))^2}\implies x=√( 36 + 113 ) \implies x=√( 149 )\implies x\approx 12.2`