How to Calculate Angle Length

Geometric calculations of angles use simple math equations. Angles are classified in three basic ways: acute (less than 90 degrees), obtuse (more than 90 degrees) and right (90 degrees). The three sides of a right triangle are called the opposite, adjacent and hypotenuse (the longest side) and are used in calculating functions of the angle. By knowing the lengths of two sides of a right triangle, the length of the third side can be determined.

Knowing characteristics of two sides of an angle can help you determine the third.

Things You'll Need

  • Ruler

  • Calculator (optional)

Step 1

Suppose you have a right triangle with two sides of known lengths and an unknown hypotenuse. Remember that a right triangle has three angle segments (or sides), the opposite, adjacent and hypotenuse. The 90-degree angle is opposite the hypotenuse.

Step 2

Label each side of the triangle with the letters a, b and c. Label the longest side, the hypotenuse, c.

Step 3

Write down the known measurements. For example, side a is 12 inches long and side b is 6 inches long. The unknown segment is side c.

Step 4

Use the Pythagorean theorem, which says that c = √(a^2 + b^2).

Step 5

Substitute numbers into the equation, so c = √12^2 + 6^2 = √(144 + 36) =√180. Do the math; in this equation, side c would be 13.4164 inches long.


Calculating angle segments using the Pythagorean theorem only works for triangles that contain a right angle. A right angle is formed when two angle segments meet to form a square or 90-degree edge.