right-triangle trig

Remember in a rt triangle   sin = opp side / hypotenuse

 

we will need to find side DC 

 

Pythag theorem    DC = sqrt (9^2 - 5^2) = sqrt 56

 

sin b =   sqrt 56  /  9 = 2 sqrt 14 / 9       = .83148   

 

 

......or you can find cos b = 5/9     then find   sinb   with the trig identity    cos^2 + sin^2 = 1

                                                                                                                      25/81  + sin^2 = 1

                                                                                                                          sin^2 = 1- 25/81

                                                                                                                                   = 56/81

                                                                                                                            sin = sqrt 56 / 9 =  2 sqrt 14 / 9        as before.....