Trig and possible vectors help

  • Thread starter mossfan563
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Homework Statement


Oasis B is a distance D = 9 km east of oasis A, along the x axis shown in the Figure. A confused camel, intending to walk directly from A to B instead walks a distance W1 = 22 km west of due south by angle θ1 = 15.0°. It then walks a distance W2 = 33 km due north. If it is to then walk directly to B, (a) how far (in km) and (b) in what direction should it walk (relative to the positive direction of the x axis)?

3_2_a.jpg


Homework Equations


Pythagorean theorem and trig.


The Attempt at a Solution


I drew a picture that depicted the camel's path. I ended up with two right triangles. I used the angle and side that I had to try and find out the length of the two sides.
W1 * sin 15
Then i subtracted whatever I got to get the remainder of W2.
W2 - (W1 * sin 15).
I also did W1 * cos 15 to find the remaining side. Then I added 9 to fill out the upper right triangle. Then I did pythagorean theorem to find out the answer for a.
I'm confused as to what angle to find for part B.

For a, I got 40.74 km and it was wrong. I redid the problem and got 49.679 and it was wrong.
For b, I got 47.93 degrees and it was wrong. Then I got 56.665 and it was wrong.

Am I doing the problem wrong?
 

Answers and Replies

  • #2
tiny-tim
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A confused camel, intending to walk directly from A to B instead walks a distance W1 = 22 km west of due south by angle θ1 = 15.0°.

W2 - (W1 * sin 15).
Hi mossfan563! :smile:

(it would be easier to help you if you actually gave all your calculation, instead of just the result)

sin = opposite/hypotenuse, so I think you should have used W2 - (W1 * cos 15).
 
  • #3
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Hi mossfan563! :smile:

(it would be easier to help you if you actually gave all your calculation, instead of just the result)

sin = opposite/hypotenuse, so I think you should have used W2 - (W1 * cos 15).
Well I assume that you know what W2 and W1 is and what not since its given in the question. But since you want all my calculations:

W1 * sin 15 = 5.69 km

W2 - (W1 * sin 15) = 27.3 km

W1 * cos 15 + 9 = 30.25 km

27.3^2 + 30.25^2 = 1660 km

sqrt(27.3^2 + 30.25^2) = 40.747 km

Why W2 - (W1 * cos 15)? W1 is the hypotenuse if you draw the triangles/camel's path correctly. 40.747 is the hypotenuse of the other triangle.
 
  • #4
tiny-tim
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Why W2 - (W1 * cos 15)? W1 is the hypotenuse if you draw the triangles/camel's path correctly. 40.747 is the hypotenuse of the other triangle.
The confused camel is going 15º west of due south.

That's very nearly due south.

So it's going very nearly 22 miles south, = 22*cos15º, to be subtracted form the 33 miles north :smile:
 
  • #5
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The confused camel is going 15º west of due south.

That's very nearly due south.

So it's going very nearly 22 miles south, = 22*cos15º, to be subtracted form the 33 miles north :smile:
So you are saying the camel's is really just a line and a triangle?
 
  • #6
tiny-tim
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So you are saying the camel's is really just a line and a triangle?
no … I'm saying that the 22*sin15º is the much shorter distance that the camel goes westward.

the camel goes mostly south and a bit west.
 

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