Hello,

I'm trying to answer this question from my textbook, but I'm getting nowhere with it.

Find the magnitude and the direction of the resultant of the two given vectors:
A displacement of magnitude 3.5 Km on a bearing of 50 degrees and a displacement of magnitude 5.4 km on a bearing of 123 degrees

The answer given in the book is 7.02 km and 98.9 degrees.

I've been going round in circles with this question for hours and I would really be grateful for any help

Have a sketch.

Draw each dsiplacement, one after the other and the resultant by joining the origin to the last point. This should give you a triangle. You need to find angles in the triangle. The top angle is 360-(123+(180-50)) = 107 degrees.

360 because a complete turn is 360.
123 is one of the three angles making 360.
180-50 is the second angle, obtained through co-interior angles of two Northern parallel lines.

Now that you got the angle, you'll have to use the cosine rule to find the magnitude of the resultant (I'll call it R)

R = \sqrt{3.5^2 + 5.4^2 - 2(3.5)(5.4)cos107}

From that, you can find the second angle in the triangle using the sine rule.

\frac{sin\theta}{5.4} = \frac{sin107}{R}

I'm having a slight difference from your given answer. Check if you copied either the information well or the answers.