Question

(Simplify your answer. Type an exact answer, using radicals as needed.)

Answer 1

This is a right-angle triangle problem and we use the Pythagoras theorem to solve it:

`\text{hypotenuse}^2=opposite^2+adjacent^2`

Given:

Adjacent side = unknown

Opposite side = 2m

Hypotenuse side = 6m

Substituting the given values above into the Pythagoras expression, we will have:

`\begin{gathered} 6^2=2^2+x^2 \\ 36=4+x^2 \\ 36-4=x^2 \\ 32=x^2 \\ \sqrt[]{32}=\sqrt[]{x^2} \\ \sqrt[]{16*2}\text{ =x} \\ \sqrt[]{16}*\sqrt[]{2}=x \\ 4*\sqrt[]{2}=x \\ 4\sqrt[]{2}=x \\ \text{The lenght of the unknown side is 4}\sqrt[]{2}m\text{ } \end{gathered}`