A boy works 10km westward and then 30 degree north of west

[Guest]

A boy works 10km westward and then 30 degree north of west, if the
displacement of the boy is 30km, 20 degree north of west from the
starting point. Find the distance travel at the second part of the
journey?

[Guest]

You have a triangle with one side of length 30 km, the angle opposite that side 180- 30= 150 degrees and a second side of length 10 km. Calling the length of third side "c", by the cosine law, [tex]30^2= 10^2- 2(10)(x)cos(150)[/tex].

[tex]900= 100- 20(-0.8660)x[/tex]
[tex]800= 17.32x[/tex]
[tex]x= \frac{800}{17.32}= 46.19[/tex]

The boy was, in a straight line, 45.19 km from his starting point.