A cruise ship travels 310 miles due east before turning 20°
north of east. It travels 150 miles along its new course. How far is the cruise ship from its initial position?
To find the total distance from the initial position, we can use the law of cosines.
Let the initial position be point A, the first destination point be point B, and the final position be point C.
From point A to point B, the cruise ship travels 310 miles due east. From point B to point C, the cruise ship travels 150 miles at an angle 20° north of east.
Using the law of cosines, we have:
AC^2 = AB^2 + BC^2 - 2(AB)(BC)cosθ
Where θ is the angle between AB and BC, which is 70° (90° - 20°)
AC^2 = 310^2 + 150^2 - 2(310)(150)cos70°
AC^2 = 96040
AC = √96040
AC ≈ 309.93 miles
Therefore, the cruise ship is approximately 309.93 miles from its initial position.