Question 935016
The Law of Sines (or Sine Rule) is very useful for solving triangles:


{{{a/sin(A)=b/sin(B)=c/sin(C)}}}

you are given:  {{{a=x}}}, {{{b=3sqrt(6)}}}, angle {{{B=60}}}, and {{{c=y}}} 

=> we also know that angle {{{A=30}}} and angle {{{C=90}}}


{{{a/sin(A)=b/sin(B)}}}


{{{x/sin(30)=3sqrt(6)/sin(60)}}}


{{{x/(1/2)=(3sqrt(2)sqrt(3))/sqrt(3)/2}}}


{{{x/(1/2)=(3sqrt(2)cross(sqrt(3)))/cross(sqrt(3))/2}}}


{{{2x=6sqrt(2)}}}


{{{highlight(x=3sqrt(2))}}}


now find {{{y}}}

{{{x/sin(30)=y/sin(90)}}}


{{{3sqrt(2)/(1/2)=y/1}}}


{{{highlight(y=6sqrt(2))}}} 


or you can use law of tan:


{{{tan(60)=3sqrt(6)/x}}}


{{{x=3sqrt(6)/sqrt(3)}}}


{{{x=(3sqrt(2)sqrt(3))/sqrt(3)}}}


{{{x=(3sqrt(2)cross(sqrt(3)))/cross(sqrt(3))}}}


{{{highlight(x=3sqrt(2))}}}


now use Pythagorean theorem to find {{{y}}}


{{{y^2=(3sqrt(2))^2+(3sqrt(6))^2}}}


{{{y^2=9*2+9*6}}}


{{{y^2=18+54}}}


{{{y^2=72}}}


{{{y=sqrt(72)}}}


{{{y=sqrt(2*6^2)}}}


{{{highlight(y=6sqrt(2))}}}