Cayce said:
Ok then here is my problem. I took this course on the basis that it was algebra based physics. We are doing sin, cos, and tan which are trig functions. I have done some tutorials on Khan academy with these functions so that I understand them since I never took trig. The last lecture we spent the entire lecture dealing with triangles so I just assumed this would be a triangle. I don't know where to even start in trying to solve this problem. I am so confused.
Each "leg" of your trip forms a vector (since it has a length and a direction). If you look from the start to the end of the vector AB for the first leg, you go ##x## units in the easterly direction and ##y## units in the northerly direction, so that single portion of the trip can be thought of as a kind of triangle: it has a base ##x## an height ##y##, and a 90 degree turn from east to north. In fact, if you walked due east by ##x## units and then due north by ##y## units, you would end up in exactly the same place as in the first leg of the trip. The hypotenuse of your little triangle is, of course, the actual leg of the trip, going off at a certain angle for a certain distance. (Note that if ##y< 0## you go ##-|y|## units north, which is actually ##+|y|## units
south. Similarly, a negative easterly step is actually a positive step in the westerly direction.)
Following that you go along another leg of your trip and so you have another vector and hence have another triangle. If you had stopped at a 2-leg trip (AB then BC) you would, indeed get a true triangle ABC whose sides are the first leg AB, the second leg BC and the total vector CA from finish to start.
However, that is NOT what you have: your trip contains a third leg CD, so now the figure ABCDA is a quadrilateral, not a triangle. (If you had made a fourth leg DE your "figure" ABCDEA would now be 5-sided, a kind of pentagon, etc.)
Anyway, for your 3-leg trip, you need to figure out the total displacement you make in the east ##(+x)## direction and the total displacement you make in the north ##(+y)## direction. That will tell you the final position after the third leg of your journey. From that you can figure out how far you are from your starting point, and what would be the angle from the start to the final point.
