To find the lengths of sides b and c in a triangle with angles A=35 degrees, B=40 degrees, and side a=3680 meters, the Law of Sines is applicable. First, calculate angle C using the sum of interior angles, which gives C=105 degrees. Then, apply the Law of Sines: a/sin(A) = b/sin(B) = c/sin(C). This allows for the calculation of sides b and c based on the known values. Using these formulas will yield the required side lengths.