Area of a triangle = (1/2)(base)(height)
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.
The disappearances of people that entered the triangle.
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".
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.
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The 3 interior angles of any triangle add up to 180 degrees
There is not enough information to solve this. You need to know one other length od a side to solve this.
Base times height divided by 2
It depends on what information you have and what information you require.