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Gnom [1K]
3 years ago
10

Seattle, WA and San Francisco, CA lie on the same longitudinal line. San Francisco is at 38° latitude and Seattle is at 47° lati

tude. 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

Mathematics
1 answer:
Helen [10]3 years ago
7 0

Step 1.

Calculate measure of angle α:

47^o-38^o=9^o

Step 2.

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

\dfrac{9^o}{360^o}=\dfrac{1}{40}

Step 3.

Calculate the circumference of the Earth (circle):

C=2\pi r\to C=2\pi\cdot4000=8000\pi\ mi

Step 4.

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

\dfrac{1}{40}C=\dfrac{1}{40}\cdot8000\pi=200\pi\ mi

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


<h3>Answer: A) 628 miles</h3>

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