Question

find the distance along an arc on the surface of earth that subtends a central angle of 18 minutes (1 minute = \\( \frac { 1 } { 60 } \\) degree). the radius of earth is 3,960 miles. round to the nearest hundredth of a mile. miles question help: message instructor

Explanation:

Step1: Convert the angle from minutes to degrees

Given \(1\) minute \(=\frac{1}{60}\) degree. So for \(18\) minutes, the angle \(\theta\) in degrees is \(\theta = 18\times\frac{1}{60}=0.3\) degrees.

Step2: Convert the angle from degrees to radians

We know that to convert degrees to radians, we use the formula \(\text{radians}=\frac{\pi}{180}\times\text{degrees}\). So \(\theta_{rad}=\frac{\pi}{180}\times0.3=\frac{\pi}{600}\) radians.

Step3: Use the arc - length formula \(s = r\theta\)

The radius of the Earth \(r = 3960\) miles and \(\theta=\frac{\pi}{600}\) radians. Then \(s=3960\times\frac{\pi}{600}\).

$$
LATEXBLOCK0
$$

Answer:

\(20.73\) miles