The opposite of angle 60° is x, to find the value of x, we can use the sine function.
[tex]\begin{gathered} \sin 60\degree=\frac{\text{opposite}}{\text{hypotenuse}} \\ \sin 60\degree=\frac{x}{4\sqrt[]{3}} \\ \\ \text{The value for }\sin 60\degree\text{ is }\frac{\sqrt[]{3}}{2} \\ \frac{\sqrt[]{3}}{2}=\frac{x}{4\sqrt[]{3}} \\ \\ \text{Multiply both sides by }4\sqrt[]{3} \\ (4\sqrt[]{3})\frac{\sqrt[]{3}}{2}=\frac{x}{4\sqrt[]{3}}(4\sqrt[]{3}) \\ \\ \text{The }4\sqrt[]{3}\text{ will cancel out in the right side} \\ (4\sqrt[]{3})\frac{\sqrt[]{3}}{2}=\frac{x}{\cancel{4\sqrt[]{3}}}\cancel{4\sqrt[]{3}} \\ \frac{4\cdot3}{2}=x \\ \frac{12}{2}=x \\ 6=x \\ \\ x=6 \end{gathered}[/tex]
Therefore, the value for x is 6 units.
To solve for y, we can use the cosine function, since y is adjacent to 60°
[tex]\begin{gathered} \cos 60\degree=\frac{\text{adjacent}}{\text{hypotenuse}} \\ \cos 60\degree=\frac{y}{4\sqrt[]{3}} \\ \\ \text{The value of }\cos 60\degree\text{ is }\frac{1}{2},\text{ substitute and multiply both sides by }4\sqrt[]{3} \\ \cos 60\degree=\frac{y}{4\sqrt[]{3}} \\ (4\sqrt[]{3})\frac{1}{2}=\frac{y}{4\sqrt[]{3}}(4\sqrt[]{3}) \\ (4\sqrt[]{3})\frac{1}{2}=\frac{y}{\cancel{4\sqrt[]{3}}}(\cancel{4\sqrt[]{3}}) \\ \frac{4\sqrt[]{3}}{2}=y \\ 2\sqrt[]{3}=y \\ \\ y=2\sqrt[]{3} \end{gathered}[/tex]
Therefore, the value of y is 2sqrt(3) units.
