How to Find the Perimeter of a Triangle With an Unknown Variable

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The perimeter of a triangle is the sum of the lengths of all of its 3 sides. If you know 2 of the side lengths of a triangle and the angle between the two, you can calculate the length of the third side and therefore find the perimeter.

Things You'll Need

  • Scientific calculator
  • Draw the picture of the triangle. It does not have to be to scale.

  • Represent one of the known side lengths with the variable 'a' and the other with the variable 'b.' Represent the measure of the angle between them with the variable uppercase 'C.'

  • Apply the law of cosines to solve for the third side. The law of cosines states c^2 = a^2 + b^2 - 2ab*cos(C). You already know a, b, and uppercase C, so it is simple to solve for lowercase c, the length of the third side.

  • Sum a, b, and lowercase c to obtain the perimeter of the triangle.

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