fine the missing side lengths for x and y

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Answer:
[tex]x=\dfrac{4\sqrt{3}}{3};\ y=\dfrac{8\sqrt{3}}{3}[/tex]
Step-by-step explanation:
The side ratios of a 30°-60°-90° triangle are ...
1 : √3 : 2
In your triangle, they are ...
x : 4 : y
In order to get these values, we need to multiply the reduced ratio by 4/√3 = (4√3)/3. Then we have ...
x : 4 : y = (4√3)/3 : 4 : (8√3)/3
and we can see that ...