Answer:
[tex]x = 8[/tex]
[tex]y=2\sqrt{3}[/tex]
Step-by-step explanation:
The figure is composed of 3 Right triangles. To find the values of the variables x and y we use the Pythagorean theorem to propose one equation.
[tex]x^2 =4^2 + (4\sqrt{3})^2[/tex]
Now we solve for x
[tex]x=\sqrt{4^2 + (4\sqrt{3})^2}[/tex]
[tex]x=\sqrt{16 +16*3}\\\\x=\sqrt{64}\\\\x=8[/tex]
Let's call z at the angle opposite to y
Then we have that:
[tex]sin(z) =\frac{opposite}{hypotenuse}[/tex]
Where
[tex]hypotenuse = 8[/tex]
[tex]opposite=4[/tex]
[tex]sin(z) =\frac{4}{8}[/tex]
[tex]z=sin^{-1}(\frac{1}{2})[/tex]
[tex]z=30[/tex]
Now we use this angle to find the length y
[tex]sin(z) =\frac{opposite}{hypotenuse}[/tex]
Where in this case
[tex]hypotenuse = 4\sqrt{3}[/tex]
[tex]opposite=y[/tex]
[tex]z=\°30[/tex]
[tex]sin(30\°) =\frac{y}{4\sqrt{3}}[/tex]
[tex]y=sin(30\°)*4\sqrt{3}[/tex]
[tex]y=2\sqrt{3}[/tex]
