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.
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There is no single formula: there are several, depending on what information you have and what you wish to know.
He defined the spherical triangle
for any spherical triangle on any sphere there associated another triangle called the polar triangle associated with this spherical triangle with the property that the sum of any angle (or side) of one of these two triangles and the length of the side (and the angle)of the other triangle is alway equil to 180 degrees
plane trigonometry spherical trigonometry
Trigonometry is the study of plane and spherical triangles. Plane trigonometry deals with 2 Dimensional triangles like the ones you would draw on a piece of paper. But, spherical trigonometry deals with circles and 3 Dimensional triangles. Plane trigonometry uses different numbers and equations than spherical trigonometry. There's plane trigonometry, where you work with triangles on a flat surface, then there's spherical trigonometry, where you work with triangles on a sphere.