Use Trigonometric Ratio to Find Missing Side

A triangle is shown.

What is the length, in inches, of side a ?

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Using one of the three main trigonometric functions is needed.

              opposite                                 adjacent                              opposite
sin  =  ------------              cos  =  -------------           tan  =  ------------
           hypotenuse                            hypotenuse                           adjacent

Side a is opposite the 30° angle.
The side that is 44 inches is the hypotenuse (the side across from the right angle).

              opposite
sin  =  -------------  will be used
            hypotenuse

                        a
Sin 30°  =  ------   {substituted given information into sin ratio}
                       44

                 a
0.5  =  ------   {evaluated sin 30° to be 0.5}
               44

a = 22 inches   {multiplied each side by 44}

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