The correct answer is A.
We can find these values by setting up proportions. We know that in a 30-60-90 triangle like this that the proportions are 1-[tex] \sqrt{3} [/tex]-2. And we know that those values line up as follows x-20-y. So we can start by making the proportion to solve for x.
[tex] \frac{1}{x} = \frac{\sqrt{3}}{20} [/tex] ---> cross multiply
[tex] \sqrt{3} [/tex]x = 20 ----> divide
x = [tex] \frac{20\sqrt{3}}{3} [/tex]
Now we can do the same for the y values.
[tex] \frac{2}{y} = \frac{\sqrt{3}}{20} [/tex] ---> cross multiply
[tex] \sqrt{3} [/tex]x = 40 ----> divide
x = [tex] \frac{40\sqrt{3}}{3} [/tex]
