Answer: Choice B
x = 9*sqrt(3) and y = 18
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Step-by-step explanation:
The short leg is given to be 9 units long. This side is opposite the smallest angle. The rule is that smallest side is opposite the smallest angle. The hypotenuse is twice as long as the short leg in a 30-60-90 triangle, so 2*9 = 18 is the hypotenuse.
The long leg is equal to sqrt(3) times the short leg
long leg = (short leg)*sqrt(3)
long leg = 9*sqrt(3)
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You can use the pythagorean theorem with a = 9 and c = 18 to solve for b
a^2 + b^2 = c^2
9^2 + b^2 = 18^2
81 + b^2 = 324
b^2 = 324 - 81
b^2 = 243
b = sqrt(243)
b = sqrt(81*3)
b = sqrt(81)*sqrt(3)
b = 9*sqrt(3)
It's a longer way to get the same answer as above for the length of the long leg.