SOLUTION: given one side of a 30-60-90 triangle how do you find the other 2 sides?

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Question 466173: given one side of a 30-60-90 triangle how do you find the other 2 sides?
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
We'll describe three cases:
1)The given side is the hypotenuse, equal a: Then the leg opposite to the 30 degree angle is a/2 and the other leg base on the Pythagorean theorem will be:
.
2)The given side is the side opposite to the 30 degree angle, equal b: Then the
hypotenuse will be 2b, and the other leg base on the Pythagorean theorem will be
sqrt%28%282b%29%5E2-b%5E2%29=sqrt%283b%5E2%29=b%2Asqrt%283%29
3)The given side is the side opposite to the angle 60 degree, equal c:
Assume that the angle opposite to the angle 30 degree is x, then the hypotenuse is 2x, and using the Pythagorean theorem we write:
c%5E2=%282x%29%5E2-x%5E2<=>c%5E2=3x%5E2<=>x=sqrt%28c%5E2%2F3%29=c%2Asqrt%283%29%2F3, and the hypotenuse will be: 2c%2Asqrt%283%29%2F3