How to add and subtract vectors (with image)

This is for my physics HW. To be clear I'm not asking for the answer, but rather how to do it. My teacher did a horrible job in explaining it.

This is the image that comes with the problem http://oi52.tinypic.com/2up3gxk.jpg
There are multiple parts to this (but it's basically the same)

Part A) Find magnitude of vector sum in A+B
Part B) Find direction of vector sum in A+B
Part C) Find magnitude of vector difference in A-B
Part D) Find direction of vector difference in A-B

Thanks in advanced for those who help.

There are 3 basic methods.
1 Geometric. Draw it accurately.
2. Trigonometric. Using multiple angle formulae
3 components.

Look at 3 which is what you are probably using.
Any vector can be resolved into two directions.
A is easy . It is purely down.
B is at 30 degrees to the vertical.
Now to find the height you get 15 * cos(30 deg) = 12.99
and the width is 15 * sin(30) = 7.5


To add A + B we add the widths
7.5 + 0 = 7.5 to the right
then the heights
12.99 - 8 = 4.99 ( the negative is used to show that it is down)
so the result is a vector with a height of 4.99 and a width of 7.5

To get the magnitude we use Pythagoras' theorem. C^2 = X^2 + y^2
= 7.5^2 + 4.99 ^2
c = sqrt( 7.5 ^ 2 + 4.99^2)
= 9.0 m


To get the angle we use triangle formulae Tan (theta) = opposite / adjacent
if measuring from the vertical line this is width /height
so theta = atan( width/height ) = atan(7.5 / 4.99)
= 56 degrees


With this as a pattern you should be able to do the other half of the question.

And please. Don't ever blame the teacher. Teachers are there to help. But in the ultimate it is always up to you. They can't do it all.

To do vector addition and subtraction you first need to break each vector into its components along the x and y axes. To take the vector B, for example, the formula to find each of the components would be this: