How to Calculate Sides of a Triangle

Calculate the sides of a triangle using the Law of Sines.
••• triangle rouge image by Unclesam from

Calculating the sides of a triangle helps you to determine the perimeter of a triangle even if you only have the measure of two of the angles and one of the sides. To find the sides of the triangle, you need to use the Law of Sines. A scientific calculator with trigonometric functions will help you to find the sine of each of the angles. According to the Law of Sines, the ratio of the sines of each angle divided by the length of the opposite side are all equal. This helps you to find the sides of the triangle.

    Add the two angles together and subtract the sum from 180 degrees to find the third angle. For instance, if angle A equals 30 degrees and angle B equals 45 degrees: 30 + 45 = 75; 180 – 75 = 105 degrees = angle C.

    Press the measure of angle B followed by the sine button on your scientific calculator. For the example: sine 45 = 0.71.

    Multiply the sine of angle B by the length of the side opposite angle A (side A). For the example, if side A measured 10 inches: 0.71 x 10 = 7.1.

    Divide this number by the sine of angle A to find the length of side B. For the example, angle A measured 30: sine 30 = 0.5: 7.1/0.5 = 14.2 inches for the length of side B.

    Repeat the procedure using angle C instead of angle B to find the measure of the side opposite angle C (side C). For the example: Multiply the sine of angle C (105) by the length of side A and divide the answer by the sine angle A (30): sine 105 = 0.97 x 10 = 9.7/0.5 = 19.4 inches for side C.

    Things You'll Need

    • 2 triangle angle measures
    • Length of one triangle side
    • Scientific calculator with trigonometric functions

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