Answer:
2 sqrt(2)
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj / hypotenuse
cos 30 = sqrt(6)/ c
c cos 30 = sqrt(6)
c = sqrt(6)/ cos 30
c = sqrt(6) / ( sqrt(3) /2)
c = 2 sqrt(6) / sqrt(3)
We cannot have a radical in the denominator
c = 2 sqrt(6) / sqrt(3) * sqrt(3)/sqrt(3)
= 2 sqrt(18)/3
We can simplify the sqrt
c = 2 sqrt(9*2) / 3
c = 2 *3 sqrt(2)/3
= 2 sqrt(2)
