In triangle ABC, angle A = 40°, angle B = 65°, and side a = 12. Find side b to the nearest tenth.

We know two angles and a side opposite one of those angles, so the Law of Sines is appropriate.

The Law of Sines states:
a / sin(A) = b / sin(B)

Substitute the known values:
12 / sin(40°) = b / sin(65°)

Solve for b by multiplying both sides by sin(65°):
b = 12sin(65°) / sin(40°)

Using a calculator in degree mode:
sin(65°) ≈ 0.9063
sin(40°) ≈ 0.6428

Substitute these approximations:
b ≈ 12(0.9063) / 0.6428

Multiply the numerator:
12(0.9063) ≈ 10.8756

Then divide:
b ≈ 10.8756 / 0.6428
b ≈ 16.9

Therefore, side b is approximately 16.9 units long.