Latitude exact relationship of parallels and meridians with horizontal and vertical: both are complicated curves. On the sphere the normal passes through the centre and the latitude () is therefore equal to the angle subtended at the centre by the meridian arc from the equator to the point concerned. If the meridian distance is denoted by then where denotes the mean radius of the Earth. is equal to . No higher accuracy is appropriate for since higher-precision results necessitate an ellipsoid model. With this value for the meridian length of 1 degree of latitude on the sphere is (60.0 nautical miles).
Triangle angles is equal to 90°, adding up to a total of 270°. Specifically, on a sphere the sum of the angles of a triangle is where "f" is the fraction of the sphere's area which is enclosed by the triangle. For example, suppose that we draw a triangle on the Earth's surface with vertices at the North Pole, at a point on the equator at 0° longitude, and a point on the equator at 90° West longitude. The great circle line between the latter two points is the equator, and the great circle line between either of those points and