# What is the direction angle of the resultant <34,-21>

#### Gummg

How do I solve this?

#### HallsofIvy

MHF Helper
The same way you solve your previous problem! You have a right triangle where one leg has length 34 and the other has (signed) length -21. Use the Pythagorean theorem to determine the length of the hypotenuse and use inverse trig functions to determine the angle.

#### Plato

MHF Helper
How do I solve this?
How does your textbook define direction angle of the resultant ?

#### Gummg

would it be inverse tan (21/34) or (-21/34)

#### Plato

MHF Helper
would it be inverse tan (21/34) or (-21/34)
Without knowing how the textbook defines things, it is hard to answer.
But if $(a,b)$ is a point then the angle determined by the position vector $<a,b>$ can be found as follows.
If $a\cdot b\ne 0$ then
$\theta=$ $\begin{cases}\arctan\left(\dfrac{b}{a}\right) &\text{ if }a>0 \\\pi+\arctan\left(\dfrac{b}{a}\right) &\text{ if }b>0~\&~a<0 \\-\pi+\arctan\left(\dfrac{b}{a}\right) &\text{ if }a<0~\&~b<0 \end{cases}$