Triangle Height Calculator
Calculate triangle heights (altitudes) using various methods and triangle types
Calculate Triangle Heights
Triangle Heights (Altitudes)
Enter positive values for all three sides
Example Calculations
Scalene Triangle (3-4-5)
Given: Sides a = 3, b = 4, c = 5
Area (Heron's): s = 6, Area = √[6×3×2×1] = 6
Heights: h_a = 2×6/3 = 4, h_b = 2×6/4 = 3, h_c = 2×6/5 = 2.4
Equilateral Triangle
Given: Side = 6 units
Formula: h = a × √3 / 2
Height: h = 6 × √3 / 2 ≈ 5.196 units
Triangle Height Formulas
General Formula
h = 2 × Area / base
Works for any triangle
Equilateral
h = a × √3 / 2
All heights are equal
Isosceles
h_base = √(a² - (b/2)²)
Height to base from apex
Right Triangle
h_hypotenuse = (leg₁ × leg₂) / hypotenuse
Legs are heights to each other
Triangle Types
Scalene
All sides and heights different
Equilateral
All sides equal, all heights equal
Isosceles
Two equal sides, heights to equal sides are equal
Right Triangle
One 90° angle, legs are heights to each other
Understanding Triangle Heights (Altitudes)
What is Triangle Height?
A triangle height (or altitude) is a line segment from any vertex perpendicular to the opposite side (or its extension). Every triangle has three heights, one from each vertex.
Key Properties:
- Every triangle has exactly three heights
- Heights are always perpendicular to their bases
- In acute triangles, all heights lie inside the triangle
- In obtuse triangles, two heights lie outside the triangle
- In right triangles, two heights are the legs themselves
Calculation Methods
Area Method
h = 2 × Area / base (most common)
Heron's Formula
Calculate area first, then use area method
Trigonometry
Use SAS area formula, then area method
Special Triangles
Direct formulas for equilateral, isosceles, and right triangles