Determine the length of x by using trigonometry in smaller triangle.
[tex]\begin{gathered} \sin 60=\frac{x}{4} \\ \frac{\sqrt[]{3}}{2}=\frac{x}{4} \\ x=2\sqrt[]{3} \end{gathered}[/tex]
Consider the larger triangle.
Determine the length of side b by using trigonometry.
[tex]\begin{gathered} \tan 60=\frac{b}{4} \\ \sqrt[]{3}=\frac{b}{4} \\ b=4\sqrt[]{3} \end{gathered}[/tex]
Consider the upper right angle triangle.
Determine the length of side y by using the trigonometric ratio.
[tex]\begin{gathered} \text{tan}30=\frac{x}{y} \\ \frac{1}{\sqrt[]{3}}=\frac{2\sqrt[]{3}}{y} \\ y=2\sqrt[]{3}\cdot\sqrt[]{3} \\ =2\cdot3 \\ =6 \end{gathered}[/tex]
