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:
[tex]\frac{y}{\sin(30)}=\frac{18}{\sin (60)}[/tex]
From this we solve for y:
[tex]\Rightarrow y=\frac{18\sin(30)}{\sin(60)}\Rightarrow y=6\sqrt[]{3}[/tex]
*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:
[tex]h=\sqrt[]{18^2+(6\sqrt[]{3})^2}\Rightarrow h=12\sqrt[]{3}[/tex]
So, the length of the longest side is 12sqrt(3) inches (Approximately 20.8 inches).
