# Direction of the vector

What is the direction, in degrees and to 2 decimal places, for the vector whose column form is $\begin{pmatrix} a & b \end{pmatrix}$ where $a = 19$ and $b = -5$? Do not give any units in your answer. Your answer must be between $-90°$ and $270°$.

I got the answer as $-75.26°$. I used

$\arctan \frac{19}{-5}$

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Is this a question? It also sounds like a homework issue. –  kcrisman Sep 11 '12 at 15:08
it is @kcrisman ! ;) –  JackyBoi Sep 11 '12 at 15:20

Draw a picture, perhaps more or less to scale. Note that the slope is "rise" divided by "run". Or, in symbols, the slope is the change in $y$ divided by the change in $x$.
@JackyBoi: Change the problem slightly to $a=19$, $b=5$. The slope is $\frac{5}{19}$: the tangent of the angle is opposite divided by adjacent. For your problem, you will want $\arctan(-5/19)$. –  André Nicolas Sep 11 '12 at 15:40