How Do You Calculate the Magnitude of the Sum of Two Vectors?

[WPCareyDevil]

Homework Statement

Vector $$\vec{A}$$ has magnitude 3.6 units; vector$$\vec{B}$$ has magnitude 5.9 units. The angle between A and B is 45°. What is the magnitude of $$\vec{A}$$ + $$\vec{B}$$?

Homework Equations

$$\Delta$$V= $$\sqrt{V^2x +V^2y}$$
"SohCahToa"

The Attempt at a Solution

I am really struggling with this for some reason. I know its just a SAS triangle.

Sin(45)=x/5.9 = opposite angle (y component, no?) =4.1719.

I tried using sqrt(4.1719^2 + 3.6^2)
where 3.6 is the x component and 4.1719 is the y component
=5.510

But, this is not correct. Basically all of my webassign problems are similar to this type, more or less complicated. Could you please point me in the right direction?


Thank you so very much for your time!
Edit: I searched but was unable to find a thread that helped. If you know of one, that would be appreciated also

 

[CompuChip]

Sin(45)=x/5.9 = opposite angle (y component, no?) =4.1719.

Mathematically, that statement is nonsense.
What you mean is, if x is the y-component of B, then
sin(45) = x / 5.9
so
x = 5.9 sin(45) = 4.1719
Let's call it B_y instead.

Similarly, what is the x-component B_x of B?

Then do the vector addition:
(A + B) = [ A_x + B_x, A_y + B_y ]
and then calculate the magnitude using the formula you gave.

 

[WPCareyDevil]

Thank you for the reply!
Ok, I now understand that I need to calculate the x and y components of each vector.

By=4.1719
Bx=[sin(45)=3.6/x]=2.5456

Ay=[sin(45)=x/3.6]=2.5456
A=[cos(45)=x/3.6]=2.5456

Therefore A=5.09117, B=6.7175

However, when I plug this into the equation I get an incorrect answer (8.4288).Can you make it a little more clear? Thank you so much for the help.

 

[WPCareyDevil]

Ok, making progress here.I split each of the two vectors up as right triangles with HypA=3.6, HypB=5.9

Ax will =Ay
and Bx will = By, because they are 45/45/90 triangles.

Ay+Ax=5.0912
By+Bx=8.3486

But those two numbers do not yield the correct answer in the formula either (9.774473).

What am I doing wrong? I have gotten other answers on my homework correct.

Do I need to use the formula twice? Ie (ax, ay), and then (bx, by) then add? Just thinking out loud