Hello, BenLaden!

Two ships, $\displaystyle A$ and $\displaystyle B$, leave port O simultaneously.

Ship $\displaystyle A$ travels due north at 16 km/h and ship $\displaystyle B$ travels due east at 13km/h.

$\displaystyle \text{Find the magnitude and direction of }\overrightarrow{AB}\text{ after:}$

. . (i) 1 hour . . (ii) 3 hours . . (iii) t hours.

The answer in the book gives the direction as 141°.

I got an answer of 39° from A.

Is this acceptable or must answer be given as 141° ?

After one hour, we have this diagram: Code:

A *
|\
| \
|θ \
16 | \
| \
| \
| \
O * - - - * B
13

You are correct . . . $\displaystyle \theta = 39^o$

But information is useless unless it is clear *where* the angle is located.

There are several methods for indicating the direction.

Here are a few of them.

[1] Bearing: measured clockwise from due North.

. . .The bearing is: .$\displaystyle 180^o - 39^o \:=\:141^o$

[2] Standard angle: measured CCW from due East.

. . .The standard angle is: .$\displaystyle -51^o$

[3] Heading: measured East or West of due North or due South.

. . .The heading is: .$\displaystyle S\:39^o\,E$

The problem should have stated the *method* of indicating the direction.