Solving a 25° North of East Walk: Exploring the Solution

[Arooj]

Homework Statement

A person walks 25 degree north of east for 3.10 km. How far would another person have to walk due north and due east to arrive at the same location?

Homework Equations

sin = opp/hyp
cos = adj/hyp

The Attempt at a Solution

I drew a line representing north of east 3.10 km at 25 degrees.
...
../.
./..
/...

I then drew the lines for north and east

/\--->
|.../
|../
|./

I used sin 25 = opp/3.10
and cos 25 = adj/3.10

and I came up with the values 1.31 for east and 2.81 for north.

However, the correct answer is 1.31 north and 2.81 east, my values were mixed up.
Can someone explain to me where I went wrong and why this is the right answer? I assumed the bottom most point on my sketch as where the 25 degrees NE, because it seemed to be going in that direction at that point.

 

[Muphrid]

You drew east of north instead of north of east.

"25 degress north of east" = start at east and turn 25 degrees towards north

 

[Muphrid]

You drew east of north instead of north of east.

"25 degress north of east" = start at east and turn 25 degrees towards north

 

[Arooj]

Thanks, I understand my problem now. This site does a good job on explaining north of east and other such directions if anyone else might get the same problem I had.
http://zonalandeducation.com/mstm/physics/mechanics/vectors/introduction/introductionVectors.html

 

[Nickie]

I would like to first clarify that the given information does not specify the starting point of the person's walk. Without knowing the starting point, it is impossible to accurately determine the distance the other person would have to walk due north and due east to arrive at the same location.

Assuming that the starting point is the same for both people, your attempt at a solution is correct. However, the mistake you made was in the interpretation of the values.

The value of 1.31 for east represents the distance the person would have to walk due east to arrive at the same location. Similarly, the value of 2.81 for north represents the distance the person would have to walk due north to arrive at the same location.

In your sketch, you have correctly drawn the line for east, but the line for north is incorrect. It should be drawn at a 25 degree angle from the east line, not from the bottom most point. This is because the person is walking 25 degrees north of east, not starting at a point 25 degrees north of east.

I hope this explanation helps clarify your confusion. It is important to carefully interpret the values and directions given in a problem to accurately solve it.