Identify the base you will use for the triangle.
Choose a height that corresponds to that base (the perpendicular distance from the opposite vertex to the base).
If you know the area (A) and base (b): use (h=frac{2A}{b}).
If you know two sides (a) and (b) and the included angle (theta): use (h=asintheta) (where (a) is the side forming the angle with the chosen base).
If you know the side lengths and the triangle is right: use (h) as the leg perpendicular to the chosen base.
If you know a side (c) and the other two sides (a) and (b) (or you can find the area via Heron’s formula): compute (A) then use (h=frac{2A}{b}).
If you have coordinates of vertices:
Use the line through the base endpoints to form the base equation.
Compute the perpendicular distance from the opposite vertex to that line using the distance-to-a-line formula.
If you know the circumradius (R) and the side (b) opposite the angle (gamma): compute the area (A=frac{abc}{4R}) then use (h=frac{2A}{b}).