What is the angle measurement of this vector?

Question

A force of 240 Newtons acts at 30 degrees. Another force of 500 Newton acts at the same point at 240 degrees. Find the resultant vector and its magnitude and angle. I got the magnitude using the pythagorean theorem. Now I don't know the degree.

Answer 1

Find new vector:

$240cos(30)+500cos(240)=-42.1539$

$240sin(30)+500cos(240)=-313.0127$

Now use $tan$ to find the degree. $arctan\frac{-313.0127}{-42.1539}$$=82$

So the angle is $82$ so $180+82=262$ since it lies in the third quadrant