Calculating Displacement with Vectors

[Angus Dolan]

Homework Statement

Hello, I have a homework question that I'm having difficulty with, it is:
A car travels due east (bearing 90) from point A for 6km to point B and then North-west (bearing 315) for 4.0km to point C.
By constructing a vector diagram, or otherwise, find the resultant displacement (magnitude and direction) of the car at point C from A.

Homework Equations

I don't think pythagoras theorem works here, as there is no right-angled triangle present. Although, I may be incorrect.

The Attempt at a Solution

I've drawn a vector diagram, head to tail, and measured the displacement, it comes to 4.3km at a bearing of 50. Is that correct?

 

[SaltyBriefs]

You can try other methods of finding vector C, you can find the components of vector A, and vector b

Remember finding the magnitude or resultant vector is
$\vec{R}$ = $\vec{A}$ + $\vec{B}$

which is really
$\vec{R}$ = (A$_{x}$ ) (B$_{x}$ ) + (A$_{y}$ ) (B$_{y}$ )

A$_{y}$ = ($\vec{A}$) (sin $\theta$)
A$_{x}$ = ($\vec{A}$) (cos $\theta$)


B$_{y}$ = ($\vec{A}$) (sin $\theta$)
B$_{x}$ = ($\vec{A}$) (cos $\theta$)

The Ax, Ay, Bx, By equations are derived from this idea

 

[SaltyBriefs]

I would plug and chug for you, but I'm kind of confused by the bearings.

 

[SaltyBriefs]

Don't rely on measuring the displacement vector. Sometimes the ruler isn't as precise, also it will help you in the long run to have these equations in your tool box.

 

[SaltyBriefs]

Let me know if you solved it, or if it helped. So I can get some personal feedback, because I don't want to be misinforming people lol.