Question

Given an arbitrary spherical triangle ABC on the unit sphere with interior angles a,b, and c, prove that the area of triangle ABC=a+b+c−π. Include a labelled diagram with your proof

Answer 1

The area of a spherical triangle ABC on the unit sphere can be calculated using the formula: Area = a + b + c - π, where a, b, and c are the interior angles of the triangle.

Step-by-step explanation:

Area = a + b + c - π

Where a, b, and c are the interior angles of the triangle.

To prove this, we can use the fact that the sum of the angles of a spherical triangle is always greater than 180 degrees. The excess angle is equal to the area of the triangle in radians. So, the area can be calculated by subtracting the excess angle (π) from the sum of the interior angles (a + b + c).

Below is a labelled diagram of a spherical triangle ABC: