Question

Find the value of each variable ( this is homework)

Answer 1

We have a right triangle, of which we know one angle measure and one of the leg's length.

We can use trigonometric ratios to find x and y.

For example, we can relate the two legs with the tangent of the angle as:

`\begin{gathered} \tan (\alpha)=\frac{\text{Opposite}}{\text{Adyacent}} \\ \tan (60\degree)=\frac{11\sqrt[]{3}}{x} \\ x=\frac{11\sqrt[]{3}}{\tan(60\degree)}=\frac{11\sqrt[]{3}}{\sqrt[]{3}}=11 \end{gathered}`

Then, we can relate x and y as:

`\begin{gathered} \cos (\alpha)=\frac{\text{Adyacent}}{\text{Hypotenuse}} \\ \cos (60\degree)=(x)/(y)=(11)/(y) \\ y=(11)/(\cos(60\degree))=(11)/((1)/(2))=11\cdot2=22 \end{gathered}`

Answer: x=11 and y=22.