Final answer:
The boat has traveled approximately 35.13 miles south from the harbor.
Step-by-step explanation:
To find the southward distance traveled by the boat, we need to understand the direction and angle provided. The bearing of S64° E implies that the boat is traveling towards the south of east at an angle of 64°. Since the boat has traveled 40 miles on this bearing, we can use trigonometry to find the southward distance traveled.
We can use the sine function to find the southward component of the distance by multiplying the distance traveled by the sine of the angle (64°). So, the southward distance traveled is 40 * sin(64°). Using a calculator, we find that the southward distance traveled is approximately 35.13 miles.