Answer:
Step-by-step explanation:
I'm going to use Physics here for this concept of vectors. Here are some stipulations I have set for the problem (aka rules I set and then followed throughout the problem):
** I am counting the 50 m as 2 significant digits even though it is only 1, and I am counting 200 as 3 significant digits even though it is only 1. 1 sig dig doesn't really give us enough accuracy, in my opinion.
** A bearing of .25 degrees is measured from the North and goes clockwise; that means that measured from the x axis, the angle is 89.75 degrees. This is the angle that is used in place of the bearing of .25 degrees.
** Due east has an angle measure of 0 degrees
Now let's begin.
We need to find the x and y components of both of these vectors. I am going to call the first vector A and the second B, while the resultant vector will be C. Starting with the x components of A and B:
so
so
and we need to add those results together. Due to the rules for adding significant digits properly, the answer is
(and remember I am counting that as 3 sig fig's even though it's only 1).
Now for the y components:
so
(which I'm counting as 2 sig fig's)
so
and we need to add those results together.
Now for the resultant magnitude:
and that gives us a final magnitude of
m
Now for the angle:
Since both the x and y components of the resultant vector are in quadrant 1, we don't need to add anything to the angle to get it right, so
![tan^{-1}(\frac{50}{200})=14](https://tex.z-dn.net/?f=tan%5E%7B-1%7D%28%5Cfrac%7B50%7D%7B200%7D%29%3D14)
The girl is 206 meters from her starting point at an angle of 14 degrees