Cleveland, Ohio, and Jacksonville, Florida, lie approximately on the same meridian. Cleveland has a latitude of 41.5° N, and Jacksonville has a latitude of 30.3° N. Find the distance between these two cities. (The radius of the earth is 3960 mi. Round your answer to the nearest mile.)

To calculate the distance between Cleveland, Ohio, and Jacksonville, Florida, along the same meridian, we can use the formula for the arc length of a circle. The formula is:

\[
\text{Distance} = r \times \Delta \theta
\]

where:
- \( r \) is the radius of the Earth (3960 miles),
- \( \Delta \theta \) is the difference in latitude between the two cities in radians.

### Step 1: Calculate the difference in latitude
Convert the latitudes from degrees to radians and find the difference:

\[
\Delta \theta = \theta_1 - \theta_2
\]

Here, 
\[
\theta_1 = 41.5^\circ \text{N}, \quad \theta_2 = 30.3^\circ \text{N}
\]

\[
\Delta \theta = 41.5^\circ - 30.3^\circ = 11.2^\circ
\]

### Step 2: Convert degrees to radians
To convert degrees to radians, use the conversion factor \( \frac{\pi}{180} \):

\[
\Delta \theta_{\text{radians}} = 11.2^\circ \times \frac{\pi}{180} \approx 0.1955 \text{ radians}
\]

### Step 3: Calculate the distance
Now, plug in the values into the arc length formula:

\[
\text{Distance} = 3960 \times 0.1955 \approx 774 \text{ miles}
\]

So, the distance between Cleveland, Ohio, and Jacksonville, Florida, is approximately **774 miles**.

Would you like more details on any of these steps or have any other questions?

Here are 5 related questions:
1. How would the distance change if we used a different value for the Earth's radius?
2. What is the significance of converting degrees to radians in this problem?
3. Can this method be used to find the distance between any two cities on the same meridian?
4. How do the concepts of latitude and longitude differ in calculating distances?
5. What assumptions are we making about the shape of the Earth in this calculation?

**Tip:** Always ensure that you convert degrees to radians when dealing with trigonometric functions or formulas in mathematics that expect radian inputs.

Learn how to calculate the distance between Cleveland, Ohio (latitude 41.5° N) and Jacksonville, Florida (latitude 30.3° N) using the arc length formula and Earth's radius (3960 miles). Understand the conversion of degrees to radians and how it applies to this problem. Suitable for high school students studying trigonometry.

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