use arc length formula to determine distance from arc PE to equator P?

Question

Assume earth is a sphere with radius OP=OE=3960 miles.
1. distance from 33, 57'N to equator
* If you could provide a short explanation I would really appreciate it. I have been stuck on this problem for quite some time. THANK YOU

Answer 1

The short explanation is that the quickest way to get to the equator, of course, is to go due south.

There are a total of 90 degrees of latitude above the equator; you're 33'57" above the equator.

A full "360 degrees" latitude constitutes the circumference. From the radius value, calculate circumference:

c = 2πr = 2π*3960

Now, the fraction of the arc you have is between 33'57" and 0'0", and this is out of 360'.

Converting 33'57" to decimal (57/60 = 0.95), we get 33.95 degrees.

Compared to the entire circumference, the ratio of this arc to the total circumference is 33.95/360 = 0.0943

So let's multiply that by the entire circumference:
(0.0943*2π*3960) =

2,346 miles


I think it's right, hope it helps!