Super simple question about vectors! Please help! Thank you!?

Question

Hi!!! I've tried this 7 times, and I keep getting 439 N as my answer, but I know that it is wrong... The book says that the answer is 929 N.

K, the overall question is that there are two forces, one being 600N and the other being 410N that form a 47 degree angle between them. Find the magnitude of the resultant and the angle that it forms with the larger force.

I can't really copy over my drawings, but I'm pretty sure that they're all right because I keep getting the same answer! Can someone PLEASE explain to me how to get the answer for this?? I know that the reason why I'm getting the ANGLE wrong is because I'm getting the magnitude wrong, so even if you can just help me with the magnitude, I can probably figure out the angle! :)

Thank you so much! I'll pick a best answer TODAY!

Never mind! I got it! Thank you! I was considering 47 as the angle opposite u + v when in fact it is 133 (43 + 88)! DUH!!!!!!!!

Answer 1

Your answer is correct !
R^2 = 600^2 + 410^2 - 2*600*410*cos(47)
and R is approx 439. That's correct.

Answer 2

Your book is correct.
First, by rotating the vectors, we can assume
the 600N force is horizontal.
Next, to add the 2 vectors, resolve them into
their x and y components, and add the components.
Then we'll compute the magnitude and angle of
the resultant.
A horizontal force of 600N has
component form 600(cos 0, sin 0) = 600(1,0)
The other force has component form
410(cos 47, sin 47)
Adding the components gives
R = (879.619, 299.855)
The magnitude of R is therefore
√(879.619² + 299.855²) = 929.32.
The angle of the resultant is
arctan(299.855/879.619) = 18.82 degrees.
Hope that helps!

Answer 3

resultant = sqrt(819^2+438^2) = 929, approximately
angle =47 - 28.1 = 18.1 degrees


The resultant is simply the diagonal of a ||-ogram. The height of the ||-ogram is 600sin47 = 438. The height is one leg of a right triangle and 410+600cos47 = 819 is the other. The hypotenuse is the resultant force

Answer 4

In polar form with r the resultant and Θ the angle with the smaller force expressed in degrees.

<600,47> +< 410, 0> =
in rectangular form;
(600cos47,600sin47) +(410,0) =(819.20,438.81)
Θ = arctan(438.81/819.2)
Θ = 28.2 degrees
r = 929.3N
Hope this helps