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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