Answer:
[tex]x=12[/tex]
[tex]y=12\sqrt{3}[/tex]
Step-by-step explanation:
We have been given diagram of a triangle. We are asked to find the values of x and y for the given triangle.
We will use law of trigonometric ratios to find the sides of our given triangle.
[tex]\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]
[tex]\text{sin}(60^{\circ})=\frac{y}{24}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{y}{24}[/tex]
[tex]\frac{\sqrt{3}}{2}\cdot 24=\frac{y}{24}\cdot 24[/tex]
[tex]\frac{\sqrt{3}}{1}\cdot 12=y[/tex]
[tex]y=12\sqrt{3}[/tex]
Therefore, the value of y is [tex]12\sqrt{3}[/tex].
[tex]\text{cos}=\frac{\text{Adjacent}}{\text{Hypotenuse}}[/tex]
[tex]\text{cos}(60^{\circ})=\frac{x}{24}[/tex]
[tex]\frac{1}{2}=\frac{x}{24}[/tex]
[tex]\frac{1}{2}}\cdot 24=\frac{x}{24}\cdot 24[/tex]
[tex]x=12[/tex]
Therefore, the value of x is 12.
