Nautical chart always true north, rather than magnetic north, towards which a compass points. Most charts include a compass rose depicting the variation between magnetic and true north. However, the use of the Mercator projection is not without its drawbacks. Mercator's technique was to make the lines of longitude parallel. On the real globe, the lines of longitude converge as one goes north or south away from the equator, until they meet at the pole. This distortion means that horizontal distances are exaggerated. Mercator's solution, imperfect as it might be, was to increase the distance between lines of latitude in proportion; in
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