History of longitude instant in time, local solar time at a location varies by one hour for every 15 degrees change of longitude (360 degrees divided by 24 hours), there is a direct relationship between time and longitude. If the navigator knew the time at a fixed reference point when some event occurred at the ship's location, the difference between the reference time and the apparent local time would give the ship's position relative to the fixed location. Finding apparent local time is relatively easy. The problem, ultimately, was how to determine the time at a distant reference point while on a ship.
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