This is a right-angle triangle problem and we use the Pythagoras theorem to solve it:
[tex]\text{hypotenuse}^2=opposite^2+adjacent^2[/tex]
Given:
Adjacent side = unknown
Opposite side = 2m
Hypotenuse side = 6m
Substituting the given values above into the Pythagoras expression, we will have:
[tex]\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\times2}\text{ =x} \\ \sqrt[]{16}\times\sqrt[]{2}=x \\ 4\times\sqrt[]{2}=x \\ 4\sqrt[]{2}=x \\ \text{The lenght of the unknown side is 4}\sqrt[]{2}m\text{ } \end{gathered}[/tex]
