# Spherical triangle vertices to spherical coordinates

Problem: Assume that the earth is a sphere of radius 5280 miles, find the length of the sides, the measure of the angles and the area of the spherical triangle with vertices A(70°N,10°E),B(10°S,100°E) and C(50°S,80°W). The earth's radius will be used as the unit of length. The spherical coordinates (r,v,u) of the three vertices are (1,10,20),(1,100,100) and (1,−80,140)

How did they obtain the spherical coordinates? meaning (r,v,u). So for example how did they get (1,10,20). I'm assuming the radius is 1 which is r, v=angle but i'm not sure why it is -80 and i have no idea what u could be.

I would match them as:

A : $10 \rm E \to v=10,\, 70 \rm N \to u=20$

B : $100 \rm E \to v = 100,\, 10\rm S \to u=100$

C : $80 \rm W \to v = -80, 50 \rm S \to u=140$

So, v is to East and is $(-180, 180)$ from a certain point, and u is to $\rm S$ and is $(0, 180)$ from north pole.

Hope it helps.

• hmm. I'm still a bit confused. So how you go from 70N-> u=20 and so on. – mika Feb 10 '15 at 2:25
• I think the N and S is measured from the equator, up to N and down to S. But U is from very top to very bottom. the north pole, where is 90N, is u=0. – PdotWang Feb 10 '15 at 2:29
• I got it. Thanks a lot! – mika Feb 10 '15 at 3:36