We will make use of the Trigonometry ratio to solve this question.
From the figure provided;
Hypotenuse side = 6
Opposite side = y
Adjacent side = x
Given angle = 60 degrees
To find side x, the suitable Trigonometry ratio to be used is the Cosine.
Thus, we have;
[tex]\begin{gathered} \text{Cos}\theta=\frac{\text{Adjacent}}{\text{Hypotenuse}} \\ \text{Cos}60=\frac{x}{6} \\ \text{cross}-\text{multiply} \\ x=6\times\cos 60 \\ x=6\times0.5 \\ x=3 \end{gathered}[/tex]
To find side y, the suitable Trigonometry ratio to be used is the Sine.
Thus, we have;
[tex]\begin{gathered} Sin\theta=\frac{\text{Opposite}}{\text{Hypotenuse}} \\ \text{Sin}60=\frac{y}{6} \\ cross-multiply \\ y=6\times\sin 60 \\ y=6\times\frac{\sqrt[]{3}}{2} \\ y=3\sqrt[]{3} \end{gathered}[/tex]
Hence, the values of x and y are:
[tex]x=3;y=3\sqrt[]{3}[/tex]
