If by sperical triangle you mean a triangle on the surface of a sphere, you will need 3 dimensional coordinate geometry. Whether you use polar coordinates or linear coordinates will depend on what you want to "solve".
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A spherical triangle is not a question or a puzzle that you can solve, or even slove! You need to specify what information you have and what you wish to solve for: angles, lengths of sides, perimeter, area and so on.
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