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Homework Statement
A plane flies from base camp to Lake A, 280 km away inthe direction 20.0°north of east. After dropping off sup-plies, it flies to Lake B, which is 190 km at 30.0°west of north from Lake A. Graphically determine the distance and direction from Lake B to the base camp.
Homework Equations
The Attempt at a Solution
I've drawn a line from base camp to lake A with an angle of 20°, another line from lake A to lake with an angle of 30°.
I have calculated the components of vector A, I already know the [tex]|A|=280km, |B|=190km[/tex], so:
[tex]A_{x}=Acos(\frac{pi}{9})=263km[/tex],
[tex]A_{y}=Asin(\frac{pi}{9})=95.8km[/tex],
[tex]B_{x}=Bsin(\frac{-pi}{6})=-95km[/tex],
[tex]B_{y}=Bcos(\frac{-pi}{6})=165km[/tex];
[tex]R^→=A^→+B^→[/tex];
[tex]|R|=sqrt((168^2)+(261^2))=310km[/tex],
[tex]cosσ=\frac{168}{310}→σ=57.2°[/tex],
[tex]sinσ=\frac{261}{310}→σ=57.4°[/tex];
I get the exact result because:
[tex]B_{x}=Bsin(\frac{-pi}{6})=-95km[/tex],
[tex]B_{y}=Bcos(\frac{-pi}{6})=165km[/tex];
i don't know why,
In which quadrant are the vector B and R?
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