A boat travels 30 miles north, 20 miles east and 40 miles northeast. What is the angle of rotation of the boats direction from start to finish

The angle of rotation of the boats direction from start to finish = 50.36⁰ to east towards north.

Step-by-step 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.