A ship 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
