# 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!!

Delta2
Homework Helper
Gold Member
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
Homework Helper
Gold Member
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
Homework Helper
Gold Member
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
Homework Helper
Gold Member
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
Homework Helper
Gold Member
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
Homework Helper
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 $+90^\circ$).