# Homework Help: Map question involving vectors (find the angle)

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1. Sep 15, 2018 at 11:09 PM

### alexi_b

1. The problem statement, all variables and given/known data
Instructions for finding a buried treasure include the following: Go 66.0 paces at 256deg, turn to 140deg and walk 125 paces, then travel 100 paces at 169deg. The angles are measured counterclockwise from an axis pointing to the east, the +x direction. Determine the resultant displacement from the starting point. Enter the distance (without units) and the angle relative to the positive x-axis.

2. Relevant equations

3. The attempt at a solution
I already figured out the displacement which is 213 paces but i thought the angle could be found using the two components (x and y), 35.4 and -210. Please help because I'm wrong!!

2. Sep 15, 2018 at 11:27 PM

### Delta²

so if you do $\tan\theta=\frac{-35.4}{210}$ the angle you get isn't the correct answer? I suspect that the answer is given in positive number , which other positive angle has the same tangent as that negative angle?

3. Sep 16, 2018 at 7:52 AM

### alexi_b

I tried that as well but it’s apparently still wrong

4. Sep 16, 2018 at 8:36 AM

### Delta²

I didn't check your answer for the displacement, is 213 paces correct?

5. Sep 16, 2018 at 8:37 AM

### alexi_b

Yes it’s 213 paces

6. Sep 16, 2018 at 8:38 AM

### Delta²

What's the answer key for the angle?

7. Sep 16, 2018 at 8:39 AM

### alexi_b

It unfortunately doesn’t say, its an online where it tells me whether I’m right or wrong

8. Sep 16, 2018 at 8:45 AM

### Delta²

So neither -9.568 degrees or 350.432 degrees is the correct answer?

9. Sep 16, 2018 at 8:48 AM

### alexi_b

Could you explain to me why it would be 350.432 degrees?

10. Sep 16, 2018 at 8:51 AM

### Delta²

Trigonometry formulas say that the tangent of angle $-\theta$ is equal to the tangent of angle $2\pi-\theta$ or $360-\theta$ in degrees.

11. Sep 16, 2018 at 10:28 AM

### alexi_b

Well i just tried 3.50 x 10^2 degrees (since i can only carry 3 significant digits) and unfortunately still a no :(,

12. Sep 16, 2018 at 10:35 AM

### Delta²

Well I don't know what else, maybe you calculated the x and y as y,x, try $\tan\theta=-\frac{210}{35.4}$ which leads to $\theta=-80.4$ or $\theta=279.6$

13. Sep 16, 2018 at 10:37 AM

### alexi_b

Thank you so much for your help I really appreciate it!

14. Sep 17, 2018 at 2:54 PM

### robphy

For the counterclockwise angle from the positive-x-axis, $\theta=\tan^{-1} \left(\frac{R_y}{R_x}\right)$,
with the rule of thumb to add $180^\circ$ if $R_x<0$ (since $\tan^{-1}$ returns a value between $-90^\circ$ and $+90^\circ$).