It means to find all of its sides and angles.
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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".
Pythagorean theorum.
It depends on the infoamtion that you have.
You cannot solve for a leg in any triangle without at least one other side.
You will also need the angles so that you can use the Isosceles Triangle Theorems to solve for the base of isosceles triangle when only two sides are given.