Question

Find the length of YZ:

Answer 1

Check the picture below.

`\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies √(c^2 - b^2)=a \qquad \begin{cases} c=\stackrel{hypotenuse}{5}\\ a=\stackrel{adjacent}{\textit{\LARGE a}}\\ b=\stackrel{opposite}{3}\\ \end{cases} \\\\\\ √(5^2 - 3^2)=a\implies √(25-9)=a\implies 4=\textit{\LARGE a} \\\\[-0.35em] ~\dotfill\\\\ \textit{using the pythagorean theorem}`

`c^2=a^2+b^2\implies √(c^2 - b^2)=a \qquad \begin{cases} c=\stackrel{hypotenuse}{8}\\ a=\stackrel{adjacent}{\textit{\LARGE b}}\\ b=\stackrel{opposite}{3}\\ \end{cases} \\\\\\ √(8^2 - 3^2)=b\implies √(64-9)=b\implies √(55)=\textit{\LARGE b} \\\\[-0.35em] ~\dotfill\\\\ YZ=\textit{\LARGE a+b}\implies YZ=4+√(55)\implies YZ\approx 11.42`