Calculate Angle C with Tail-Tip Method

[Confused one]

I have 2 vectors, which are plotted using the tail-tip method to form a non-right triangle.

Side A is vector 1, side B is vector 2, and side C is my resultant.
I know I can get angle C, but that's where I'm stuck.

How do you get angle C? In simple terms...

 

[HallsofIvy]

It's a bit confusing to talk about "side C" and "angle C"! Standard notation is that the lengths of the three sides of the triangle are a, b, c and the angles opposite each are A, B, C respectively. If you know a, b, c, then use the cosine law to find C: c²= a_{2[/sup]+ b²- 2ab cos(C). Plug in a, b, c and solve for C.}

 

[Confused one]

I don't have c. I have a, b, and their degrees, but no c. I don't have A or B either.

I'm trying to sove for C, but I must have c before I can use the law of cosines.

 

[mathmike]

how about law of sins

sin A / a = sin B / b = sin C / c

 

[HallsofIvy]

You orginally said "Side A is vector 1, side B is vector 2, and side C is my resultant" so it was reasonable to assume that you knew those 3 lengths. In vector problems, normally you know two vectors, say lengths a and b, and the angle between them, but that would be C which you say you don't know. If lengths a and b are the only values you have, you can't solve this: two parts of a triangle are not enough! What information do you have?

 

[Werg22]

You have to understand that the resultant vector components are the sum of the adding vectors. Add the vertical component of the vector A to the vertical component of vector B. Then add the horizontal component of the vector A to horizontal component of vector B. Then you have the components of vector C and the magnitude of C = ((Ay + By)^2 + (Ax + Bx)^2)^1/2

 

[HallsofIvy]

You have to understand that the resultant vector components are the sum of the adding vectors. Add the vertical component of the vector A to the vertical component of vector B. Then add the horizontal component of the vector A to horizontal component of vector B. Then you have the components of vector C and the magnitude of C = ((Ay + By)^2 + (Ax + Bx)^2)^1/2

That's one way to do it. It may or may not be simpler than adding the vectors "geometrically". The question "Confused one" initially asked made it clear, I thought, that he was attempting to do this geometrically. I sure wish he would get back to us and tell us exactly what information he has to work with. I would have suggested that he find angle C by just subtracting the angles the the vectors make with some fixed line, but surely he wouldn't be having so much trouble if he were given the vectors like that.