Question

Find the value of x and y (picture attached) (choose one option)A. x=12, y=24B. x=24, y=12C. x=12, y=12✓3D. x=24, y=12✓3E. x=12✓2, y=24

Answer 1

The value of x and y is;

`\begin{gathered} x=12 \\ y=24 \end{gathered}`

Step-by-step explanation:

Given the Triangle in the attached image.

To get the value of x and y. Let us apply trigonometry;

`\sin \theta=(opposite)/(Hypotenuse)`

For x;

`\begin{gathered} \sin 45=\frac{x}{12\sqrt[]{2}} \\ x=12\sqrt[]{2}\sin 45 \\ \sin 45=\frac{1}{\sqrt[]{2}} \\ So; \\ x=12\sqrt[]{2}*\frac{1}{\sqrt[]{2}} \\ x=12 \end{gathered}`

Now, that we have the value of x, let us solve for y;

`\begin{gathered} \sin 30=(x)/(y) \\ y=(x)/(\sin 30) \\ x=12\text{ and }\sin 30=0.5 \\ So; \\ y=(12)/(0.5) \\ y=24 \end{gathered}`

Therefore, the value of x and y is;

`\begin{gathered} x=12 \\ y=24 \end{gathered}`

A