Any section made by a cutting plane that passes through a sphere is circle. A is formed when the cutting plane passes through the center of the sphere. Spherical triangle is a triangle bounded by arc of great circles of a sphere.
Note that for spherical triangles, sides a, b, and c are usually in angular units. And like plane triangles, angles A, B, and C are also in angular units.
Sum of interior angles of spherical triangle
The sum of the interior angles of a spherical triangle is greater than 180° and less than 540°.
$180^\circ \lt (A + B + C) \lt 540^\circ$
Area of spherical triangle
The area of a spherical triangle on the surface of the sphere of radius R is given by the formula
In spherical trigonometry, earth is assumed to be a perfect sphere. One minute (0° 1') of arc from the center of the earth has a distance equivalent to one (1) nautical mile (6080 feet) on the arc of great circle on the surface of the earth.