Thread: Finding magnitude of u + v help?

Hey all!

I was taking a quiz for my trig class and the following problem came up:

Find the sum of u + v, given that |u| = 16, |v| = 16, and Theta = 106°.

The magnitude of u + v is: 19.3

The resultant vector u + v makes the angle 53.0 with u.

When I tried the problem, I got 22.6 for the magnitude and 45° for the angle.

I thought that r = sqrt(u^2 + v^2), and I could use arctan=(16/16) to find the angle (at least that's what my math teacher had said).

Any help on how they got these solutions?

Doing what you have done only works if the vectors are at right angles to each other, which these aren't. (Basically, you have used the Pythagoras theorem.)
Draw a diagram with the two vectors angled at 106 degrees to each other and draw in the vector u + v. Use the cosine rule to calculate the magnitude of u + v followed by the sine rule to calculate the angle.

Originally Posted by ktelyn

Hey all!
I was taking a quiz for my trig class and the following problem came up:
Find the sum of u + v, given that |u| = 16, |v| = 16, and Theta = 106[FONT=arial]°.
The magnitude of u + v is: 19.3[COLOR=#0000ff]

The correct answer is 19.258.

Using the law of cosines and the supplement of the angle between

I think I know what I did wrong, LOL!

I thought I had to put the angle they provided for the cosA part, but in reality I have to use the supplement.