Find the distance along an arc on the surface of the earth that subtends a central angle of 8 minutes (1 minute = 1/60 degree). The radius of the earth is 3960 miles. Round to the thousandths. (3 decimal places)
Your answer is    miles.

To find the distance along an arc on the surface of the Earth that subtends a central angle of 8 minutes, we can use the formula for arc length:

\[
s = r \theta
\]

Where:
- \( s \) is the arc length
- \( r \) is the radius of the Earth
- \( \theta \) is the central angle in radians

### Step 1: Convert the angle from minutes to degrees
Given that 1 minute = \( \frac{1}{60} \) degrees, we convert 8 minutes into degrees:

\[
8 \, \text{minutes} = 8 \times \frac{1}{60} = \frac{8}{60} = 0.1333^\circ
\]

### Step 2: Convert the angle from degrees to radians
To convert degrees to radians, use the formula:

\[
\theta (\text{radians}) = \theta (\text{degrees}) \times \frac{\pi}{180}
\]

Substitute \( \theta = 0.1333^\circ \):

\[
\theta = 0.1333 \times \frac{\pi}{180} \approx 0.002327 \, \text{radians}
\]

### Step 3: Calculate the arc length
Now, use the formula \( s = r \theta \), with \( r = 3960 \, \text{miles} \) and \( \theta = 0.002327 \, \text{radians} \):

\[
s = 3960 \times 0.002327 \approx 9.217 \, \text{miles}
\]

### Final Answer:
The distance along the arc is approximately **9.217 miles**.

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Would you like further clarification or details? 

Here are 5 related questions to explore:
1. How do you convert angles from degrees to radians?
2. What is the relationship between arc length, radius, and angle?
3. How do you convert between different units of angular measurement (e.g., minutes to degrees)?
4. What are other real-world applications of arc length calculation?
5. How would the arc length change if the angle were doubled?

**Tip**: Always ensure angles are in radians when using formulas involving arc length and circular motion!

Find the distance along an arc on the surface of the earth that subtends a central angle of 8 minutes (1 minute = 1/60 degree). The radius of the earth is 3960 miles. Round to the thousandths. (3 decimal places)

Discover how to calculate the distance along an arc on the Earth's surface that subtends a central angle of 8 minutes. Using the Earth's radius of 3960 miles, this problem involves converting angles from degrees to radians and applying the arc length formula. Ideal for students in Grades 9-11, the solution is rounded to 9.217 miles.

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