Find the length of the missing side in the triangle. (Assume b = 11.6 cm and c = 18.9 cm. Round your answer using the rules for working with

If it's a right triangle ( with a 90 degree angle) then it's simple. Just use pythagorean theorem.

$${{\mathtt{a}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{b}}}^{{\mathtt{2}}} = {{\mathtt{c}}}^{{\mathtt{2}}}$$

in your case you need variable a, so :

$${{\mathtt{a}}}^{{\mathtt{2}}} = {{\mathtt{c}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{{\mathtt{b}}}^{{\mathtt{2}}}$$

Then you just put in the numbers :

$${{\mathtt{a}}}^{{\mathtt{2}}} = {{\mathtt{18.9}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{{\mathtt{11.6}}}^{{\mathtt{2}}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{a}} = {\mathtt{\,-\,}}{\frac{{\sqrt{{\mathtt{4\,453}}}}}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5}}}}\right)}}\\
{\mathtt{a}} = {\frac{{\sqrt{{\mathtt{4\,453}}}}}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5}}}}\right)}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{a}} = -{\mathtt{14.921\: \!461\: \!054\: \!467\: \!823\: \!1}}\\
{\mathtt{a}} = {\mathtt{14.921\: \!461\: \!054\: \!467\: \!823\: \!1}}\\
\end{array} \right\}$$

Because it's a lenght it can't be negative value, therefore a = -14.9xxx can't be a valid answer. Answer is :

$${\mathtt{a}} = {\frac{{\sqrt{{\mathtt{4\,453}}}}}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5}}}}\right)}} \Rightarrow {\mathtt{a}} = {\mathtt{14.921\: \!461\: \!054\: \!467\: \!823\: \!1}}$$

And then you round it up to your necessary amount.

Cheers

We need to know what kind of triangle we have......if it's a right triangle, are these the legs???