# Map question involving vectors (find the angle)

## Homework Statement

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.

## 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!!

## Answers and Replies

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Delta2
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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?

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

Delta2
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I didn't check your answer for the displacement, is 213 paces correct?

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

Delta2
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What's the answer key for the angle?

What's the answer key for the angle?
It unfortunately doesn’t say, its an online where it tells me whether I’m right or wrong

Delta2
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So neither -9.568 degrees or 350.432 degrees is the correct answer?

So neither -9.568 degrees or 350.432 degrees is the correct answer?
Could you explain to me why it would be 350.432 degrees?

Delta2
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Trigonometry formulas say that the tangent of angle $-\theta$ is equal to the tangent of angle $2\pi-\theta$ or $360-\theta$ in degrees.

Trigonometry formulas say that the tangent of angle $-\theta$ is equal to the tangent of angle $2\pi-\theta$ or $360-\theta$ in degrees.
Well i just tried 3.50 x 10^2 degrees (since i can only carry 3 significant digits) and unfortunately still a no :(,

Delta2
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Gold Member
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 $\theta=279.6$

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 $\theta=279.6$
Thank you so much for your help I really appreciate it!

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 $+90^\circ$).