Vector Help?

Question

Vector A is 3.0 units in length and points along the poisitive x-axis; vector B is 4.0 units in length and points along a direction 150* from the positive x-axis. What is the magnitude of the resultant when vectors A and B are added?

a. 7.0
b. 6.7
c. 4.7
d. 2.1

If you can please plug in the numbers too...I tried figuring it out and Im getting a little confused

Answer 1

A = (3, 0)
B = (4cos150°, 4sin150°) = (4*(-√3/2), 4*(1/2))
B = (-2√3, 2)

A + B = (3 - 2√3, 0 + 2) = (3 - 2√3, 2)

The magnitude of the resultant is:

|| A + B || = √[(3 - 2√3)² + 2²] = √(9 - 12√3 + 12 + 4)

|| A + B || = √(25 - 12√3) ≈ 2.0531416

Answer 2

This Q is just a basic trig Q. First, draw it and label the sides a, b, and c. Label the angles opposite the letters with the equivalent capital letter. Then use the law of cosines. I labeled the unknown side a.

a^2=b^2+c^2-2bc(cosA)
Plug in the #'s and you get
a^2=4^2+3^2-2(4)(3)(cos30)
Put that in your trusty calculator and you'll end up with
a^2=4.29
and then square root it to get 2.1