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Seattle, WA and San Francisco, CA lie on the same longitudinal line. San Francisco is at 38° latitude and Seattle is at 47° latitude. If the earth is a sphere of radius 4000 miles, use arc length to find the distance between the cities. [Use π = 3.14, and round to the nearest mile.]

A) 628 miles
B) 725 miles
C) 786 miles
D) 841 miles

Seattle WA and San Francisco CA lie on the same longitudinal line San Francisco is at 38 latitude and Seattle is at 47 latitude If

Answer :

Step 1.

Calculate measure of angle α:

[tex]47^o-38^o=9^o[/tex]

Step 2.

Calculate what fraction of the angle 360° ​​is the angle α:

[tex]\dfrac{9^o}{360^o}=\dfrac{1}{40}[/tex]

Step 3.

Calculate the circumference of the Earth (circle):

[tex]C=2\pi r\to C=2\pi\cdot4000=8000\pi\ mi[/tex]

Step 4.

The length of arc is equal 1/40 of the circumference:

[tex]\dfrac{1}{40}C=\dfrac{1}{40}\cdot8000\pi=200\pi\ mi[/tex]

[tex]\pi\approx3.14\to\dfrac{1}{40}C\approx200\cdot3.14=628\ mi[/tex]


Answer: A) 628 miles

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Rewritten by : Barada

Final answer:

The question uses geometry and the concept of arc length to ask the distance between Seattle and San Francisco on the Earth's surface. The distance between the two cities is calculated to be 628 miles.

Explanation:

This is a mathematics problem using geometry, specifically related to the calculation of the arc length. The difference in latitudes between Seattle and San Francisco gives us the angle measurement on the sphere's surface. The difference is 47° - 38° = 9°. Since 9° is 1/40th of a full circle (360°), the arc is 1/40th of the total circumference.

So, to find the distance between the two cities, we calculate 1/40th of the circumference of the Earth (which is 2πr) by using the given radius of the Earth (4,000 miles). The calculation is 1/40 * 2 * 3.14 * 4000 = 628 miles. So, The distance between Seattle and San Francisco via the arc length on the sphere's surface is approximately 628 miles.

Therefore, the correct answer is A) 628 miles.

Learn more about Arc Length here:

https://brainly.com/question/37703789

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