Question

In the right triangle shown, m∠A = 30 degrees, and BC = 6√2, how long is AC?

Answer 1

They're trying to trick you with √2.  Remember in the 30/60/90 triangle the sides are in ratio 1:√3:2, with the "1" opposite the 30 degrees.

Here we have

1:√3:2  = 6√2:x:hypotenuse

or

x/(6√2) = √3/ 1

x = 6√2×√3 = 6√6

Answer: AC=6√6