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a.
x = 10/3, y = 30
b. x= 10, y = 30-3
c. x= 30/3, y=10
d. x = 30, y = 10.73

A X 103 Y 30 B X 10 Y 303 C X 303 Y10 D X 30 Y 1073 class=

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Answer:

d. [tex]\displaystyle x = 30, y = 10\sqrt{3}[/tex]

Step-by-step explanation:

In a 30°-60°-90° triangle, the shorter leg is represented by [tex]\displaystyle x,[/tex]the longer leg is represented by [tex]\displaystyle x\sqrt{3},[/tex]and the hypotenuse is represented by [tex]\displaystyle 2x.[/tex] So, evaluate:

[tex]\displaystyle hypotenuse \hookleftarrow 2x \\ long\:leg \hookleftarrow x\sqrt{3} \\ short\:leg \hookleftarrow x \\ \\ 20\sqrt{3} = 2x\:[x\:is\:'y'\:in\:this\:case]; 10\sqrt{3} \\ \\ \\ x\sqrt{3} = x \\ \\ 30 = 10\sqrt{3}[\sqrt{3}][/tex]

In the end, you arrive at this:

[tex]\displaystyle x = 30, y = 10\sqrt{3}[/tex]

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