How Can You Calculate the Magnitude of Vector A Using Dot Product Rules?

[rambo5330]

Homework Statement

i'm having troubles solving this problem in physics involving dot product rule


Vector B is 5m and 60 degress above the x axis
A has the same magnitude as C and C is has 25 more degrees than A ..
find magnitude of A..
B dot C = 35
B dot A = 30

this all we're given.. as far as i can get it i make it down to two equations
cos(\theta + 25) = 7/C and cos(\theta) = 6/C

 

[rl.bhat]

The two equations should be

cos(θ-60 + 25) = 7/c...(1)
cos(θ-60) = 6/c ...(2)
divide (1) by (2), you get

\frac{cos(\theta-60 + 25))}{cos(\theta-60)} = 7/6

Let (θ - 60) = x
expand cos(x + 25) and divide it by cos(x)and simplify to find x.

 

[rambo5330]

excellent thank you,

I thought that was the method but I'm still running into trouble expanding cos(x + 25) and dividing to clear... when i expand i get


cosx / (cos(x))(cos(25)) - (sin(x))(sin(25)) = 6/7

i don't see how dividing that by cos(x) now accomplishes anything?

where am i going wrong?

 

[rambo5330]

nm its all good i got it figured out thanks !