How to Calculate Sides of an Angle

Angles are geometrical entities nestled between intersecting lines. Make those lines and the point where they cross a part of a recognized geometric structure, and you can take advantage of the properties of that structure to characterize the lines. The process can be as simple as adding a single line. Adding this line encloses the angle in a triangle, and converts the intersecting lines to the sides of a triangle. By applying triangle geometry and the relationships that govern triangles, you can then calculate the length of the intersecting lines.

Things You'll Need

  • Ruler
  • Protractor
  • Calculator
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Instructions

    • 1

      Label the angle formed between the intersecting lines with the uppercase letter C, and measure angle C using the protractor.

    • 2

      Label the lines that intersect to form angle C with lowercase letters a and b.

    • 3

      Join the free ends of the lines a and b with a third pencil line so that a triangle is formed. Label this third line with the lowercase letter c. Measure the length of c.

    • 4

      Label the angle opposite to line b as angle B, and the angle opposite to line a as angle A. Measure angles A and B using the protractor.

    • 5

      Find the unknown side lengths a and b using this relationship: a/(sin A) = b/(sin B) = c/(sin C). First calculate c/(sin C) as both length c and angle C are known. Equate c/(sin C) to a/(sin A) to find the length a. Equate c/(sin C) to b/(sin B) to find the length b. For example, start with an angle (C) of 60 degrees and draw side c with length 10 cm, so that the triangle you create has measured angles A = 45 degrees, and B = 75 degrees. Side length a = (sin A) x (c)/(sin C) = (sin 45) x (10)/(sin 60) = 8.16 cm. Side length b = (sin B) x (c)/(sin C) = (sin 75) x (10)/(sin 60) = 11.15 cm.

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