Question

1. a motorcycle traveled 750 miles at 70 degrees south of east. how far south did the motorcycle travel?

○ 317 miles south
○ 704.8 miles south
○ 256.5 miles south
○ 724.4 miles south

Explanation:

Answer:

To determine how far south the motorcycle traveled, we use trigonometry. The distance traveled south is the opposite side of the right triangle formed by the displacement vector (750 miles) and the angle of 70 degrees south of east.

The formula for the opposite side (south distance) is:
\[
\text{South distance} = 750 \times \sin(70^\circ)
\]

Calculating this:
\[
\sin(70^\circ) \approx 0.9397
\]
\[
750 \times 0.9397 \approx 704.8
\]

So the correct option is: 704.8 miles south