How do you calculate the angle between two sides in an equilateral triangle?

The angle between two sides in an equilateral triangle is always 60 degrees.

In an equilateral triangle, all three sides are of equal length, and all three internal angles are equal. Since the sum of the internal angles in any triangle is always 180 degrees, you can divide this total equally among the three angles in an equilateral triangle. Therefore, each angle is 180 degrees divided by 3, which equals 60 degrees.

To understand why this is the case, consider the properties of an equilateral triangle. By definition, an equilateral triangle has three sides of the same length. This symmetry means that each angle must also be the same, as the triangle is perfectly balanced. If one angle were different, the sides opposite those angles would not be equal, contradicting the definition of an equilateral triangle.

You can also use basic geometric principles to verify this. If you draw an equilateral triangle and then draw a line from one vertex to the midpoint of the opposite side, you create two 30-60-90 right triangles. In these right triangles, the angles are 30 degrees, 60 degrees, and 90 degrees. Since the original equilateral triangle is composed of two such right triangles, the angle between any two sides of the equilateral triangle must be 60 degrees.

This consistent 60-degree angle is a fundamental property of equilateral triangles and is crucial for solving various geometric problems and proofs involving these shapes.