Special right triangle are in the ratio 1 : 2 : 3 and respectively measure 30° (), 60° (), and 90° (). The sides are in the ratio 1 : : 2. The proof of this fact is clear using trigonometry. The geometric proof is: The 30°–60°–90° triangle is the only right triangle whose angles are in an arithmetic progression. The proof of this fact is simple and follows on from the fact that if "α", , are the angles in the progression then the sum of the angles = 180°. After dividing by 3, the angle must be 60°. The right angle
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