Step 1: Analyse the given question. Draw a figure from the given information.

              Given that:

                  The boat cross a river

                  The angle between the boat and bank = 60\degree

                    From the figure:

                         AB is a bank of the river    

                         Boat starts at A.                         

                         Angle between the bank of the river and way of the boat \angle CAB = 60\degree.

                         Traveled distance AC = 600 m

                         Determine the width of the river BC = ?

Step 2: Select the appropriate trigonometric ratio to find the width of the river.  

                 We need to find the width of the river (opposite side)

                                So, take \sin\ A=\frac{opposite\ side}{hypotenuse}

                                              \sin60\degree=\frac{BC}{AC}=\frac{BC}{600}

                                                      \frac{\sqrt{3}}{2}=\frac{BC}{600}.    (Since \sin60\degree=\frac{\sqrt{3}}{2})

                                                    BC=\frac{600\sqrt{3}}{2})

                                                     BC = 300\sqrt{3}

                                        Hence, the width of the river   BC = 300\sqrt{3}