Triangle - Angle

The Triangle Angle calculator computes the interior angle (AA) of a triangle given the length of the three sides (a, b & c).

INSTRUCTIONS: Choose units and enter the following:

• (a) the length of side a
• (b) the length of side b
• (c) the length of side c

Triangle Angle (AA): The calculator returns the angle in degrees.  However, this can be automatically converted to other angle units (e.g. radians) via the pull-down menu.

The Math/Science

This is derived from the following equation:

`tan("AA"/2) = sqrt( ((s-b)(s-c)) / (s*(s-a)) )`     where the semi-perimeter: `s = (a + b + c)/2`

A triangle is a polygon with three sides, three vertices (corners), and three angles. Triangles can be classified based on the lengths of their sides and the measures of their angles as follows:

By Side Lengths:

• Equilateral Triangle: All three sides are equal in length.
• Isosceles Triangle: Two sides are equal in length.
• Scalene Triangle: All three sides have different lengths.

By Angle Measures:

• Acute Triangle: All three angles are less than 90 degrees.
• Right Triangle: One angle is exactly 90 degrees.
• Obtuse Triangle: One angle is greater than 90 degrees.

The sum of the interior angles of any triangle always adds up to 180 degrees. 

Triangle Calculators

• Area of Triangle (base and height)
• Area of Triangle (two sides and interior angle)
• Area of Triangle (two angles and interior side)
• Area of Triangle (three sides)
• Area of Equilateral Triangle
• Area of Triangle (three points)
• Height of Triangle
• Width of Triangle
• Triangle Perimeter
• Interior Angle of a triangle based on the length of three sides
• Semi-perimeter of a triangle
• Area of Circle Within a Triangle
• Area of Circle Around a Triangle
• Area between two vectors
• Triangle Volume

References

• Light and Matter(Dr. Benjamin Crowell) Chapter 0.12 Summary