Trig help (part 2)?

Question

okay here was my last question...If you helped me with the last question, just read the bottom, as I have a question concerning it.

Trigonometry for Physics help (cos, sin, tan)?

okay, we are doing some problems for physics..and im kind of lost...I need help because I have never taken a trig class in my life and this physics book I have doesnt help that much..heres the question.

1. A man walks 5 mi east, then 6 mi North and then 3 mi further East. Make a scale diagram of the man's path on graph paper.

I did this and got 14 mi.

part b) Calculate the straight-line distance from where the man started to where the man ends up. (Is this the same, grater than or less than your answer to part a.

I got 10 mi as my answer which is less than.

Now heres my trouble.

c) At his final position the man turns and points toward his starting point. What direction is he pointing? (Be clear and exact)

Im going to add the rest after I post this because im running out of characters

okay now heres my question, you guys helpe me get the top angle by telling me to use inverse tangent, which I understand..but the question asks for the exact direction he is facing which facing his starting point. Wouldnt this be different than the angle? The angle would be facing more towards the opposide side wouldnt it? Or is it impossiable to get the exact direction to that point? Im just having a hard time understanding if the northern angle points towards the starting point or towards the opposite side...thanks for the help

okay I think I may have it...tell me if this is right... inverse tan would give me the angle directly to the starting point,

inverse sin would give me the direction direcly south

and im not sure what inverse cos would give me...not that the problem cares about that, but Im just a bit confused as to where you would use the others. would cos give me the exact degrees to the opposite side?

Answer 1

He is facing 233 degrees, which is 180 (south) plus 53.

Answer 2

I don't have a calculator in front of me so I can't give you the exact answer but here is a way to envision it. Your graph is broken into 4 quadrants, numbered 1-4 in a clockwise direction with #1 being to the top right of the vertical axis. Since you travelled North and East in your example, this is the quadrant you would be in. The direction you would be facing when looking back at your starting point ( the origin) would to the South and West of your current position. The exact direction (bearing) would be the top angle you described expressed as that number off the vertical axis. Ex: S 45 W.
Hope this helps.