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jwj11

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**[SOLVED] Simple Vector Sum Problem... But My Calculated Angles Weird...**

## Homework Statement

A car travels 210 m [N32°E] and then travels 37 m [S51°W]. How far is the car from the origin?

## Homework Equations

Cosine Law.

C^2=A^2+B^2-2(A)(B)(CosC)

Sine Law.

C/CosC=A/CosA

## The Attempt at a Solution

C^2=210^2+37^2-(2)(210)(37)(Cos7)

C=173m

173/Sin7=37/Sin(theta)

Theta=1.5 Degrees

32 Degrees + 1.5 Degrees = [N33.5E]

Resultant solution = 173m [N33.5E]

I'm not sure if I got this question right... although I am sure that the magnitude is correct. However when I try to solve for all of the angles of the triangle, it does not add up to 180 Degrees. The problem is kind of funky because the angles are so small.

Can anyone tell me why the angles don't add up to 180 degrees... I have checked my solution 3 times but I still don't get where I could of made a mistake.

In fact, after I find out all the angles and add up I get this.

8.5 Degrees + 1.5 Degrees + 7 Degrees = 17 Degrees... That is way lower than 180.

I don't know how the hell I am getting 8.5 Degrees. I think it is because of some sine rule that I don't know, because 1.5 + 7 degrees = 8.5 degrees.

Can anyone explain this to me? Why is my calc saying 8.5 degrees instead of 171.5 Degrees.

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