Question

Find the length of the third side. If necessary, write in simplest radical form.

Answer:
3√5
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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=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{9^2-(3√(5))^2}=a\implies √(81-3^2(5))=a \\\\\\ √(81-9(5))=a\implies √(81-45)=a\implies √(36)=a\implies \boxed{6=a}`