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

Answer:

The value of x and y is;

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

Explanation:

Given the Triangle in the attached image.

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

$\sin \theta=\frac{opposite}{Hypotenuse}$

For x;

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

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

$\begin{gathered} \sin 30=\frac{x}{y} \\ y=\frac{x}{\sin 30} \\ x=12\text{ and }\sin 30=0.5 \\ So; \\ y=\frac{12}{0.5} \\ y=24 \end{gathered}$

Therefore, the value of x and y is;

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

A