SPHERICAL TRIGONOMETRY
Spherical Triangle
Any section made by a cutting plane that passes
through a sphere is circle. A great circle 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°.
Area of spherical triangle
The area of a spherical triangle on the surface of the sphere of radius R is given by the
formula:
Spherical excess
Note:
Spherical Triangle
Any section made by a cutting plane that passes
through a sphere is circle. A great circle 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°.
Area of spherical triangle
The area of a spherical triangle on the surface of the sphere of radius R is given by the
formula:
Spherical excess
Note:
