Question

2. Find the length of MN in the triangle below. M A. 2√23 B. 3√13 C. 4√6 D. 8√2 ​

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}{24}\\ a=\stackrel{adjacent}{22}\\ o=\stackrel{opposite}{MN} \end{cases} \\\\\\ MN=√( 24^2 - 22^2) \implies MN=√( 92 )\implies MN=2√(23)`