Trigonometric functions relate the lengths of a triangle's sides and the size of its angles. You can calculate the length of any of the triangle's sides from the size of its opposite angle and the ratio between any other length and opposite angle. Mathematicians call this relationship the law of sines. This trigonometric method has applications with real-life vector problems, such as how to pilot an aircraft while countering the wind.
Find the sine of the angle opposite of the length that you know. If you do not have a scientific calculator, they are available online at Web sites such as web2.0calc.com. If the angle is, for instance, 35 degrees: sin (35) = 0.574.
Divide that known length by the sine of its opposite angle. If the length measures six inches divide six by 0.574 to get 10.45.
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Find the sine of the angle opposite to the unknown length. If this angle is, for instance, 80 degrees: sin (40) = 0.643.
Multiply together the answers from steps two and three: 10.45 x 0.643 = approximately 6.7. The unknown dimension is 6.7 inches.