Use the formula for area: Height = (2 × Area) ÷ Base
If you know the area and base, substitute the values into the formula
If the triangle is right-angled, the two perpendicular sides are the height and base
If you know two sides and the included angle, use trigonometry: Height = Side × sin(angle)
If you know all three sides, first find the area using Heron’s formula, then use Height = (2 × Area) ÷ Base
If the triangle is isosceles, split it into two right triangles and use the Pythagorean theorem to find the height
If the triangle is equilateral, use Height = (√3 ÷ 2) × side length