Question

fine the values of x and y write the answer in simplest form

Answer 1

We have the following:

We know that the angle formed with the 150 ° angle is equal to 180 ° in total, therefore, the interior angle is

$\begin{gathered} 180=150+\theta \\ \theta=180-150 \\ \theta=30 \end{gathered}$

Now by means of the trigonometric ratio sine, we can calculate the value of y, which is the hypotenuse of the triangle, like this

$\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \text{replacing} \\ \sin 30=\frac{5}{y} \\ y=\frac{5}{\sin 30} \\ y=10 \end{gathered}$

now for x, we can calculate it with the trigonometric ratio cosine, which relates the adjacent leg with the hypotenuse

$\begin{gathered} \cos \theta=\frac{\text{adjacent}}{\text{hypotenuse}} \\ \text{replacing} \\ \cos 30=\frac{x}{10} \\ x=10\cdot\cos 30 \\ x=8.66 \end{gathered}$

The value of x is 8.66, the value of y is 10