We will find the length of the longest side as follows:
*First: We can see that the other angle that is missing is 60°. Now, using the law of sines we find the other side of the triangle [Not the longest yet], that is:

From this we solve for y:
![\Rightarrow y=(18\sin(30))/(\sin(60))\Rightarrow y=6\sqrt[]{3}](https://img.qammunity.org/2023/formulas/mathematics/college/wdtflvkoiv555r2e4q3bnj8qwv9ev8wzvu.png)
*Second: Now that we have the measure of the other side of the triangle (6sqrt3, approximately 10.4 inches) we find the measure of the largest side:
![h=\sqrt[]{18^2+(6\sqrt[]{3})^2}\Rightarrow h=12\sqrt[]{3}](https://img.qammunity.org/2023/formulas/mathematics/college/1lrqvvg7c3gq3puau08zp4due6te9gfw4g.png)
So, the length of the longest side is 12sqrt(3) inches (Approximately 20.8 inches).