Course of traveling

Question

A ship is traveling with speed 12km/h in North direction.A wind with speed 9km/h with direction from West to East changes the direction of ship. a)Find resultant speed (Answer.15km/h in course 36.9°) b) The sheep need to traveling back to starting point. In which course need to be her orientation? (Answer 253,7°)

(I think that a) is easy of course just a Pithagoras theorem and definition of tan.but I not have any idea at point b))

Answer 1

Draw a line segment of length $12$ from the origin to $(0, 12)$ to represent the ship's movement (of its own).
Draw a line segment of length $9$ from $(0,12)$ to $(9, 12)$ to represent the wind.

The length of the line segment connecting the origin $(0,0)$ and $(9, 12)$ can be found by the Pythagorean Theorem, as you noticed. This is a right triangle with legs of length $12$ and $9$.

As for the heading/bearing, you have to understand the convention:

• Due North is a bearing of $0^\circ$
• Due East is a bearing of $90^\circ$
• Due South is a bearing of $180^\circ$
• Due West is a bearing of $270^\circ$

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Edit: As you have pointed out, the question is likely asking for what course the ship should set, not what it's actual path will be. So the ship will need to aim for $(-9, 0)$ in order to arrive at the origin. This would result in a right triangle with sides $18$ and $12$.

I meant to add earlier - for all such questions, you should definitely draw a triangle (or two)!