Spherical Triangle

A spherical triangle is a part of the surface of a sphere bounded by three great circles.

The vertices of the drawn spherical triangle can be varied by dragging the mouse with pressed mouse button. On the right side you can read the sizes of the sides and angles. (Only proper spherical triangles are considered here, i.e.only sides and angles less than 180° occur.)

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Plane triangles are known to have a sum of angles which is exactly 180°. The sum of angles in a spherical triangle, on the other hand, can have any value between 180° and 540°: For very small spherical triangles the sum is only a little higher than 180°. For very large spherical triangles covering almost half of the sphere's surface the sum of angles is nearly 540°.

180° < α + β + γ < 540°

For the sum of the side lengths the following inequality is valid:

0° < a + b + c < 360°

Note: The numerical values are rounded to three decimal digits. If 540.000° is displayed for the sum of angles or 360.000° for the sum of side lengths, the real value is slightly smaller.