Barrow, Alaska $$ \left(71.3^{\circ} \mathrm{N}, 156.8^{\circ} \mathrm{W}\right) $$, and Kailua, Hawaii $$ \left(19.7^{\circ} \mathrm{N}, 156.1^{\circ} \mathrm{W}\right) $$, have approximately the same longitude, which means that they are roughly due north-south of each other. Use the difference in latitude to approximate the distance between the cities. Assume that the Earth is approximately spherical with radius 3960 mi . Round intermediate calculations to 5 decimal places and round your answer to the nearest mile.

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1. Compute the difference in latitude between the two cities:
   $$
   \Delta \text{lat} = 71.3^\circ - 19.7^\circ = 51.6^\circ
   $$

2. Convert the difference in latitude from degrees to radians:
   $$
   \Delta \text{lat (radians)} = 51.6^\circ \times \frac{\pi}{180} \approx 0.90053 \text{ radians}
   $$

3. Use the formula for arc length on a circle:
   $$
   \text{Arc Length} = r \times \theta
   $$
   where $$ r = 3960 $$ mi and $$ \theta \approx 0.90053 $$ radians.

4. Calculate the distance:
   $$
   d \approx 3960 \times 0.90053 \approx 3565.72680 \text{ miles}
   $$

5. Rounding to the nearest mile, the distance is:
   $$
   \boxed{3566 \text{ miles}}
   $$
The distance between Barrow, Alaska, and Kailua, Hawaii, is approximately 3,566 miles.

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