Notice that the given right triangle has a marked angle measuring 30^(∘). Therefore, by the Triangle Angle Sum Theorem the measure of the third angle must be 60^(∘).
In a 30^(∘)-60^(∘)-90^(∘) triangle, the longer leg is sqrt(3) times the length of the shorter leg.
x=sqrt(3) * 6=6sqrt(3)
We found that the measure of the longer leg is 6sqrt(3). Also, in a 30^(∘)-60^(∘)-90^(∘) triangle, the hypotenuse is 2 times the length of the shorter leg.
y= 2 * 6 ⇔ y=12
