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The longest side of the triangle will always be opposite the largest angle, which is 90° in this case. We can use the sine law to work out the other sides with that:

sin(90°) / 18 = sin(60°) / x = sin(30°) / y

1/18 = sin(60°) / x

x = 18 sin(60°)

x = 18√3 / 2

x = 9√3

1/18 = sin(30°) / y

y = 18 sin(30°)

y = 9

So the triangle has a sides of 9 and 9√3, with a hypotenuse of 18

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Q: What are the lengths of the missing sides of a 30-60-90 triangle if the longer leg of the triangle is 18 centimeter?
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