Map question involving vectors (find the angle)

[alexi_b]

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.

Homework Equations

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!

 

[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?

 

[alexi_b]

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]

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

 

[alexi_b]

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

Yes it’s 213 paces

 

[Delta2]

What's the answer key for the angle?

 

[alexi_b]

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]

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

 

[alexi_b]

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]

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

 

[alexi_b]

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]

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 $\theta=279.6$

 

[alexi_b]

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 $+90^\circ$).