# Map question involving vectors (find the angle)

• alexi_b
In summary, to find the buried treasure's resultant displacement, go 66.0 paces at 256deg, turn to 140deg and walk 125 paces, then travel 100 paces at 169deg.
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.

## 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!

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?

Delta² said:
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

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

Delta² said:
I didn't check your answer for the displacement, is 213 paces correct?
Yes it’s 213 paces

What's the answer key for the angle?

Delta² said:
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

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

Delta² said:
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?

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

Delta² said:
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 :(,

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##

Delta² said:
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!

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 $+90^\circ$).

## 1. What is a vector?

A vector is a mathematical quantity that has both magnitude and direction. It is represented by an arrow pointing in the direction of the vector with a length proportional to its magnitude.

## 2. How do you find the angle between two vectors?

To find the angle between two vectors, you can use the dot product formula: θ = cos^-1 (a · b / |a| * |b|), where a and b are the two vectors and |a| and |b| represent their magnitudes. Alternatively, you can also use the cross product formula: θ = sin^-1 (|a x b| / |a| * |b|).

## 3. What is the difference between scalar and vector quantities?

Scalar quantities only have magnitude, while vector quantities have both magnitude and direction. Examples of scalar quantities include temperature and mass, while examples of vector quantities include velocity and force.

## 4. Can vectors be added or subtracted?

Yes, vectors can be added or subtracted using the parallelogram method. This involves placing the two vectors tip to tail and drawing a diagonal between the starting point of the first vector and the end point of the second vector. The resulting diagonal represents the sum or difference of the two vectors.

## 5. How are vectors used in mapping?

Vectors are used in mapping to represent different geographical features such as roads, rivers, and boundaries. They can also be used to show the direction and magnitude of movement, such as wind direction and speed. Vectors are also used in map projections to accurately represent the curved surface of the Earth on a flat map.

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