The longer leg of a 30°-60°-90° triangle is 18. What is the length of the other

Mathematics
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The longer leg of a 30°-60°-90° triangle is 18. What is the length of the other leg?

a.6√3

b.9√3

c.9

d.12√3

Apr 30th, 2015

Let the length of the shorter leg be 'x'.

The hypotenuse of the 30°-60°-90° is 2x

18%5E2%2Bx%5E2=%282x%29%5E2 --> 324%2Bx%5E2=4x%5E2 --> 3x%5E2=324 --> x%5E2=324%2F3 --> x%5E2=108
Since the length of a segment cannot be a negative number, the only solution is

x=sqrt%28108%29=sqrt%2836%2A3%29=sqrt%2836%29%2Asqrt%283%29=6sqrt%283%29


Please let me know if you have any other questions and best me if you are satisfactory. 

Apr 30th, 2015

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