• The sides of spherical triangles are segments of great circles. That is, they are segments of the trace on the surface of the sphere of a plane defined by the two endpoints of the triangle’s side and the origin of the sphere
• The sum of the internal angles of a spherical triangle is not always 180^o.
• The law of cosines for a spherical triangle is:

  Cos(a) = cos(b)*cos(c) + sin(b)*sin(c)*cos (A)

  Where a, b, c are the angular lengths of the sides of a spherical triangle and A, B, C are the opposing internal angles (Figure)

• The law of sines for a spherical triangle is:
  

  Sin (a)/Sin (A) = Sin (b)/ Sin (B) = Sin (c)/ Sin(C) (Figure)
  

Want some practice? Set up a table in Excel and use the spherical law of cosines to find the distance between Missoula (47^oNorth, 114^o West) and the places in the table below. Convert minutes to degrees and make diligent use of absolute references:

Where?	Longitude	Latitude
Abu Dhabi	54 degrees 28’ E	24 degrees 15’ N
Port Moresby	147 degrees 20’ E	9 degrees 34’ S
Thule	68 degrees 47’ W	76 degrees 34’ N
Santiago	70 degrees 4’ W	33 degrees 26’ S
Beijing	116 degrees 23’ E	39 degrees 55’ N

State the distance in radians, degrees, and kilometers. Assume the radius of Earth is 6,371 km, which is the radius of an equal-volume sphere.