How to Do the Law of Sine on a Calculator


The law of sines relates the size of a triangle's angles and the lengths of its sides. According to the law, a single ratio links each length and the sine of its opposite angle. Unlike other methods for calculating a triangle's dimensions, the law of sines works for all triangles, regardless of their configuration. To calculate an unknown side using the law of sines, you just need a scientific calculator that finds the sines of angles.

  • Press your calculator's "sin" button.

  • Type in the size of an angle that's opposite a side whose length you know. With this example, imagine an angle of 40 degrees, so press the "4" and "0" keys.

  • Press the division key.

  • Type in the length of the known side. If, for instance, the side measures 10 inches, press the "1" and "0" keys.

  • Press the the equals key. The answer will appear on the screen. With this example, the answer is "0.06427876096865."

  • Press the "sin" key again.

  • Type in the size of the angle opposite to the length you want to calculate. For example, if this angle is 60 degrees, press the "6" and "0" keys.

  • Press the division key.

  • Press the "Ans" key if your calculator has one. Otherwise, type in the ratio that you previously calculated (0.06427876096865).

  • Press the equals key. The calculator will display the length of the unknown side, which in this example is about 13.47 inches.

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