Question

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.]

Answer 1

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:

`(9^o)/(360^o)=(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:

`(1)/(40)C=(1)/(40)\cdot8000\pi=200\pi\ mi`

`\pi\approx3.14\to(1)/(40)C\approx200\cdot3.14=628\ mi`

Answer: A) 628 miles