Triangle Height Calculator
Calculate triangle altitude using multiple methods
Triangle Diagram
About Triangle Height
The height (or altitude) of a triangle is the perpendicular distance from a vertex to the opposite side (or the line containing the opposite side). Every triangle has three different heights, one from each vertex.
Methods to Find Height
- From Area and Base: h = 2A / b
- From Side and Angle: h = side × sin(angle)
- From Three Sides: First find area with Heron's formula, then h = 2A / b
- Right Triangle: For right triangles, the legs are heights to each other
Properties
- Height is always perpendicular to the base
- A triangle has three heights, one from each vertex
- All three altitudes meet at a point called the orthocenter
- In acute triangles, the orthocenter is inside the triangle
- In obtuse triangles, the orthocenter is outside the triangle
- In right triangles, the orthocenter is at the right angle vertex
Frequently Asked Questions
What is the height of a triangle?
The height (altitude) is the perpendicular distance from a vertex to the opposite side (called the base). It forms a 90° angle with the base.
How do I calculate height from area?
Rearrange the area formula: Area = ½ × base × height, so height = 2 × Area / base.
How many heights does a triangle have?
Every triangle has three heights, one from each vertex perpendicular to the opposite side.
Can the height be outside the triangle?
Yes, in obtuse triangles, two of the three heights lie outside the triangle. The height is still perpendicular to the extended base line.
What is the orthocenter?
The orthocenter is the point where all three altitudes (or their extensions) intersect. Its location depends on the triangle type.
Are all three heights different?
In scalene triangles, all three heights are different. In isosceles triangles, two heights are equal. In equilateral triangles, all three heights are equal.