Equilateral Triangle Height

\[h=\frac{\sqrt{3}}{2}a\]

Variables

htriangle height (m)

aside length of the equilateral triangle (m)

This formula calculates the height of an equilateral triangle from the length of one side.

An equilateral triangle has three equal sides and three equal angles of 60°. The altitude divides the triangle into two identical right triangles.

The formula is derived using the Pythagorean theorem and basic trigonometric relationships.

Use this formula when:

- The triangle is equilateral

- The side length is known

- The height must be calculated

- Solving geometry or design problems

- Working with symmetrical triangular structures

This formula provides a direct and efficient calculation of the altitude.

If:

a = 10 m

Then:

h = (√(3)*10)/2

h ≈ 8.66 m

- Geometry and trigonometry

- Architecture and design

- Structural engineering

- Construction calculations

- CAD and 3D modeling

- Educational mathematics