How to Calculate Angle Length

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Things You'll Need

  • Ruler

  • Calculator (optional)

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

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.


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.

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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.



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