Trigonometry?
Arraynot found.Assuming that Earth is a sphere of radius 6378 kilometers, what is the difference in the latitudes of Syracuse, New York, and Annapolis, Maryland, where Syracuse is 450 kilometers due north of Annapolis?
Thanks.
450/(2?•6378) = 0.0112 of circumference =
0.0112 of 360° =
4.0425°
The central angle in radians is the surface distance divided by the earth radius.
Therefore, the angle subtended by the two cities at the earth center is
ang = 450/6378 radians.
This is the latitude difference since the cities are at the same longitudes (nort/south of each other)
Draw a circle.
On the right half of the circle put two different dots. The upper dot is Syracuse and the lower is Annapolis. (Obviously, this won’t be to scale.)
Label the arc between them 450km.
Draw the radii to the dots and label them 6378km.
Determine the central angle ?:
? = arclength×180/(?r)
= 450×180/(?6378)
= 4°
If you want to see the drawing, go to my profile and click on the Photobucket link.