Help With Physics Vector Problem

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The discussion revolves around solving a physics vector problem involving a cyclist's journey with multiple segments. The cyclist travels 3.7 km west and then 6.6 km at an angle of 57º west of north, ultimately ending up 2.3 km at 10º south of east from the starting point. The user expresses uncertainty about their calculations and seeks assistance in verifying their work. However, they later confirm that they successfully solved the problem. The thread highlights the importance of vector addition and direction in physics problems.
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Homework Statement



Someone bikes 3.7 km due west, and then 6.6 km at 57º west of north. The person continues for an unknown distance in an unknown direction. He ends up 2.3 km at 10º south of east of where he started.
Find the magnitude and specific direction of the third part of the person's trip.

Homework Equations



Ax = Acosθ
Ay = Asinθ
a2 + b2 = c2
tanθ = y/x

The Attempt at a Solution



kd2838.png

I have a feeling that something isn't checking out. If someone can take a look over that work and see if I've gone wrong somewhere, that would be great.

Thanks in advance for the help!
 
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I just did the problem. It is fine.
 
Thread 'Correct statement about size of wire to produce larger extension'

Thread 'Correct statement about size of wire to produce larger extension'

The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...
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