Question

how do you find a missing side with trigonometry

Answer 1

Example 1:  The angle is 42 deg and the length of the hypotenuse is 25.  The side of length x is opposite the 42 deg angle.  
                                opposite side
Thus, sin 42 deg = --------------------  =>  25 sin 42 deg = x = opp side
                                         25

                                                                25(0.669) = 16.7 units (answer)