Answer:
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 x axis be north direction.
The boat first travels 30 miles north
⇒ Displacement = 30 j
Then boat travels 20 miles east
⇒ Displacement = 20 i
And at last the boat travels 40 miles north east
⇒ Displacement = 40·cos 45 i + 40·sin 45 j
= 28.28 i + 28.28 j
Total displacement = 48.28 i + 58.28 j
[tex]\text{Angle, tanθ = }\frac{58.28}{48.28}[/tex]
⇒ θ = 50.36⁰
Hence, The angle of rotation of the boats direction from start to finish = 50.36⁰ to east towards north.
