Hello from MrBillDoesMath!
Answer:
x = 4 sqrt(3)
y = 8 sqrt(3)
Discussion:
Either via the properties of a 30-6-90 triangle, or by simple trigonometry:
tan(30) = x/12 => tan(@) = side opposite angle/ side adjacent angle
x = 12 * tan(30)
x = 12 * (1/sqrt(3))
x = 12 / sqrt(3) => multip num and denom by sqrt(3)
x = 12 ( sqrt(3)/3) => 12/ 3 = 4
x = 4 sqrt(3)
As sin(@) = side opposite angle\hypotenuse
sin(30) = x/y => multiply both sides by y
y sin(30) = x => divide both sides by sin(30)
y = x/ sin(30) => but x = 4 sqrt(3), sin(30) = 1/2
y = (4 *sqrt(3))/ 1/2 =>
y = (4*2) sqrt(3)
y = 8 sqrt(3)
Thank you,
MrB
