This is all about similarity. You don't even really need the cosine thing. It doesn't really matter too much except to tell you that you also have the length of the hypotenuse. If the cosine of that angle is 8/37, but the side adjacent to the reference angle is 8, that means that we have reduced our cosine ratio from its original numbers. Since 8 is half of 16, that means 37 is half the length of the hypotenuse in the smaller triangle. Its actual measure is 37*2 which is 74. Similarity here tells us the triangles exist in a 1:2 ratio, or that the smaller is half the size of the larger and the larger is then twice the size of the smaller. That makes the hypotenuse of the larger twice the size of the smaller. So 74*2 = 148, choice B from above.
