Answer:
The angle of rotation of the boats direction from start to finish = 50.36⁰ to east towards north.
Explanation:
Let x axis be east direction and Y axis be north direction.
We have first boat travels 30 miles north
Displacement = 30 j
20 miles east
Displacement = 20 i
40 miles northeast
Displacement = 40 cos 45 i + 40 sin 45 j = 28.28 i + 28.28 j
Total displacement = 48.28 i + 58.28 j
Angle, tanθ = 58.28/48.28
θ = 50.36⁰
The angle of rotation of the boats direction from start to finish = 50.36⁰ to east towards north.