SOLUTION: Identify the values of the variables. Give your answers in simplest radical form. http://my.thinkwell.com/questionbank/95001-96000/95690/img/238257.jpg

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Question 935016: Identify the values of the variables. Give your answers in simplest radical form.
http://my.thinkwell.com/questionbank/95001-96000/95690/img/238257.jpg
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The Law of Sines (or Sine Rule) is very useful for solving triangles:

a%2Fsin%28A%29=b%2Fsin%28B%29=c%2Fsin%28C%29
you are given: a=x, b=3sqrt%286%29, angle B=60, and c=y
=> we also know that angle A=30 and angle C=90

a%2Fsin%28A%29=b%2Fsin%28B%29

x%2Fsin%2830%29=3sqrt%286%29%2Fsin%2860%29

x%2F%281%2F2%29=%283sqrt%282%29sqrt%283%29%29%2Fsqrt%283%29%2F2

x%2F%281%2F2%29=%283sqrt%282%29cross%28sqrt%283%29%29%29%2Fcross%28sqrt%283%29%29%2F2

2x=6sqrt%282%29

highlight%28x=3sqrt%282%29%29

now find y
x%2Fsin%2830%29=y%2Fsin%2890%29

3sqrt%282%29%2F%281%2F2%29=y%2F1

highlight%28y=6sqrt%282%29%29

or you can use law of tan:

tan%2860%29=3sqrt%286%29%2Fx

x=3sqrt%286%29%2Fsqrt%283%29

x=%283sqrt%282%29sqrt%283%29%29%2Fsqrt%283%29

x=%283sqrt%282%29cross%28sqrt%283%29%29%29%2Fcross%28sqrt%283%29%29

highlight%28x=3sqrt%282%29%29

now use Pythagorean theorem to find y

y%5E2=%283sqrt%282%29%29%5E2%2B%283sqrt%286%29%29%5E2

y%5E2=9%2A2%2B9%2A6

y%5E2=18%2B54

y%5E2=72

y=sqrt%2872%29

y=sqrt%282%2A6%5E2%29

highlight%28y=6sqrt%282%29%29