How to Calculate Angle Length

Written by bobbye alley
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How to Calculate Angle Length
Knowing characteristics of two sides of an angle can help you determine the third. (Dynamic Graphics Group/Dynamic Graphics Group/Getty Images)

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.

Skill level:

Things you need

  • Ruler
  • Calculator (optional)

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  1. 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.

  2. 2

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

  3. 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.

  4. 4

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

  5. 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.

Tips and warnings

  • 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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