Question

1. a motorcycle traveled 750 miles at 70 degrees south of east. how far south did the motorcycle travel? 317 miles south 724.4 miles south 256.5 miles south 704.8 miles south

Explanation:

Step1: Identify the sine function

The distance south \(d_{south}\) can be found using the sine function. If the motorcycle travels a distance \(r = 750\) miles at an angle \(\theta=70^{\circ}\) south of east, then \(d_{south}=r\sin\theta\).

Step2: Calculate the value

Substitute \(r = 750\) and \(\theta = 70^{\circ}\) into the formula \(d_{south}=r\sin\theta\). We know that \(\sin(70^{\circ})\approx0.9397\). So \(d_{south}=750\times\sin(70^{\circ})\approx750\times0.9397 = 704.8\) miles.

Answer:

704.8 miles south