There is no single formula: there are several, depending on what information you have and what you wish to know.
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It's an equilateral triangle whose legs are all 90-degree arcs. Here's a quadrantal triangle on the earth: -- Start at the north Pole. -- Draw the first side, down along the north 1/2 of the Prime Meridian to the equator. -- Draw the second side westward along the equator, to 90 degrees west longitude. -- Draw the third side straight north, back up to the north Pole. Each side of the triangle is 90 degrees, each interior angle is also 90 degrees, and the sum of its interior angles is 270 degrees. Pretty weird.
Three non-collinear points do not determine a unique spherical triangle.
A plane triangle looks like a common triangle. A plane triangle is solved with linear units. A spherical triangle is found inside of a sphere. This type of triangle is solved with angular units.
All three interior angles of a spherical triangle may be right angles.
He defined the spherical triangle