Is There More Than One Way to Solve a Trivial Vector Problem?

[guyvsdcsniper]

Homework Statement

Graphically determine the resultant of the following three vector displacements: (1) 24 M, 36 degrees north of east; (2) 18 m, 37 degrees east of north; and (3) 26 m, 33 degrees west of south.

Relevant Equations

Vy=Vsintheta
Vx=VCostheta

I got the attached photo from someone who solves physics problems on youtube. As you can see their final answer is 6.7i+16j. I understand how she got these values but I came out with something slightly different. I solved for the x and y components on the opposite side of each vector. So basically I came out with 16i+6.7j. Both answers make sense but I believe it comes down to a matter of perspective.

I searched around on the internet and I see that many people took different approaches to this problem resulting in people either getting my answer or the attached answer.

Are they both technically right? It feels as though that a lot of these physics problems come down to a matter of perspective.

 

[haruspex]

Homework Statement:: Graphically determine the resultant of the following three vector displacements: (1) 24 M, 36 degrees north of east; (2) 18 m, 37 degrees east of north; and (3) 26 m, 33 degrees west of south.
Relevant Equations:: Vy=Vsintheta
Vx=VCostheta

I got the attached photo from someone who solves physics problems on youtube. As you can see their final answer is 6.7i+16j. I understand how she got these values but I came out with something slightly different. I solved for the x and y components on the opposite side of each vector. So basically I came out with 16i+6.7j. Both answers make sense but I believe it comes down to a matter of perspective.

I searched around on the internet and I see that many people took different approaches to this problem resulting in people either getting my answer or the attached answer.

Are they both technically right? It feels as though that a lot of these physics problems come down to a matter of perspective.

It depends on how you are relating $\hat i$ and $\hat j$ to compass directions.
The usual would be i for E and j for N.
On that basis, what do you think the i component of "24 m, 36 degrees north of east" is? There is only one correct answer.
It might help if you compare with zero degrees N of E. Does sin or cos give the right answer?

 

[guyvsdcsniper]

It depends on how you are relating $\hat i$ and $\hat j$ to compass directions.
The usual would be i for E and j for N.
On that basis, what do you think the i component of "24 m, 36 degrees north of east" is? There is only one correct answer.
It might help if you compare with zero degrees N of E. Does sin or cos give the right answer?

The i component should be the adjacent side of that angle which would come out to be 24*cos(36). Is that correct? I've attached my work as reference (my apologies for it being a bit messy).

So would that mean the original attached image is wrong?

 

[haruspex]

24*cos(36)

Yes.
The working in the image in post #1 is wrong.

 

[guyvsdcsniper]

Yes.
The working in the image in post #1 is wrong.

Thank you!