Identify the values of the variables. give your answers in simplest radical form.

x   = 5 sqrt(6)/3

 y= 10 sqrt(6)/3

Step-by-step explanation:

We know sin 60 = opposite/hypotenuse

    sin 60 = 5 sqrt(2) /y

 Multiply each side by y

y sin 60 = 5 sqrt(2)

Divide each side by sin 60

y sin 60/ sin 60 = 5 sqrt(2)/ sin 60

y = 5 sqrt(2) / sin 60

y = 5 sqrt(2) / sqrt(3) /2)

y   = 10 sqrt(2)/ sqrt(3)

You cannot leave a sqrt in the denominator

 y=   10 sqrt(2)/ sqrt(3) * sqrt(3)/sqrt(3)

   y= 10 sqrt(6)/3

tan 60 = oppositve/ adjacent

tan 60 = 5 sqrt(2)/ x

Multiply each side by x

x tan 60 = 5 sqrt(2)

Divide by tan 60

x = 5 sqrt(2)/tan 60

x =5 sqrt(2)/sqrt(3)

You cannot leave a sqrt in the denominator

x = 5 sqrt(2)/sqrt(3) * sqrt(3)/sqrt(3)

x   = 5 sqrt(6)/3