## woleraymond 3 years ago The resultant of vectors A and B has a magnitude of 20units. A has a magnitude of 8units and the angle between A and B is 40 degrees. calculate the magnitude of B?

1. rs32623

\[(8^{2}+B^{2}+2*8*B*Cos40)=20^{2}\] Can you proceed from here finding the value of B?

2. Vincent-Lyon.Fr

Use ruler and compass. You will get the value you need, then use geometry. Either resolve your vectors or work out magnitude directly using following link: http://en.wikipedia.org/wiki/Law_of_cosines

3. woleraymond

@rs32623 which formula are u using?

4. Vincent-Lyon.Fr

He is using the Law of cosines I mentioned above.

5. rs32623

i am using the formula for the resultant of two vectors A & B having magnitude A & B & angle between them if theta then the resultant is R=sqrt(A^2+B^2+2*A*B*Costheta)

6. woleraymond

i think the preferred solution is Resultant = \[sqrt{A^2 + B^2}\]

7. Vincent-Lyon.Fr

But this is true if and only if vectors A and B are at right angles.

8. woleraymond

if it is cosine rule then it should be R=sqrt(A^2+B^2-2*A*B*Costheta)....do you guys agree....@Vincent-Lyon.Fr @rs32623

9. Vincent-Lyon.Fr

You should end up with B = 13.20