6.9
1) As we can see here, this is a right triangle. So we can make use of the Pythagorean Theorem.
2) So let's write it:
[tex]\begin{gathered} a^2=b^2+c^2 \\ 13^2=11^2+c^2 \\ 169=121+c^2 \\ 169-121=c^2 \\ c^2=48 \\ \sqrt[]{c^2}=\sqrt[]{48} \\ c=\pm4\sqrt[]{3}, \\ c=4\sqrt[]{3}\approx6.9 \end{gathered}[/tex]
Note that there are no negative dimensions. So we keep the positive one and round off to the nearest tenth the answer is 6.9
