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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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