Aship travels due west for 90 miles and turns to travel 80 miles in the northwest direction at a 120 degree angle. how far is the ship from its original position

We breakdown the components of the distances.
(1) 90 miles west.
                          x - component = -90 miles
                          y - component = 0 miles
(2) 80 miles, northwest (120°)
                          x - component = (80 miles)*(sin 30°) = 40 miles (negative)
                          y - component =(80 miles)*(cos 30°) = 69.282 miles (positive)

Solve for the distance,
                                 √(-90 - - 40)² + (69.282 miles)²  = 147.31 miles