Spherical Geometry #2 - Spherical triangles and angles

So what's a spherical triangle ? We know that a normal triangle lies on a plane. Spherical triangles, on the other hand, lie on a sphere. The sides of a spherical triangle lie on great circles. The triangle ABC in the figure shown is a spherical triangle.

Image result for spherical triangle
Spherical angles: 

The angles of the spherical triangle, ie, spherical angles are defined as follows.  Consider two sides of the triangle. Draw tangents at the meeting point of the two sides in the plane of the two sides. The angle between the tangents is called the angle between the two sides.

Properties of a spherical triangle :

1. Unlike a normal triangle, the angles of a spherical triangle don't add up to 180°. In fact the sum of the angles of a triangle always adds up to more than 180° but is always less than 540°.

2. So each angle of a spherical triangle is always less than 180°.

3. Sum of any two sides of the triangle is always greater than the third side.

More posts coming soon....











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