Finding magnitudes of vectors given angles

[randomhobo]

Homework Statement

Vector A points in the negative direction. Vector B points at an angle of 35.0 above the positive axis. Vector C has a magnitude of 16 and points in a direction 44.0 below the positive axis.
Given that A+B+C=0 , find the magnitudes of A and B .

Homework Equations

A_x cos θ
A_y sin θ

The Attempt at a Solution

I think I have the picture of the triangle graphed out, but since there are no 90 degree angles, how do I use the relevant equations to find the magnitudes?

 

[CompuChip]

Homework Equations

A_x cos θ
A_y sin θ

That's not an equation, it's just a formula with some variables and a cosine.
Maybe you can look up precisely what formula you wanted to write there and explain to us what it means?
(This is not to be strict about the rules; but if you mean what I think you mean, then understanding what that formula says is the key to the solution)

Also, can you post the complete question? You just defined A, B and C, and you have to calculate the missing magnitudes, if I understand it correctly, but that is not enough info.

 

[brushman]

Try using the law of sines (I believe this works).

 

[DrewBlay]

Thanks for this, very helpful



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[rwisz]

As a scientist, the first step in solving this problem would be to draw a clear and accurate diagram representing the given information. This will help visualize the vectors and their directions.

Next, we can use the given information and the relevant equations to solve for the magnitudes of A and B. Since vector A points in the negative direction, its magnitude will be negative. Using the equation for the x-component of a vector, we can write:

Ax = -|A|cos θ

where θ is the angle between vector A and the positive x-axis. Similarly, for vector B, we can write:

Bx = |B|cos(90° - 35.0°) = |B|sin 35.0°

where 90° is the angle between vector B and the positive x-axis, and 35.0° is the angle given in the problem. We can also use the given magnitude of vector C to write:

Cx = |C|cos(90° - 44.0°) = |C|sin 44.0°

Now, since the sum of the three vectors is equal to zero, we can write the following equation:

Ax + Bx + Cx = 0

Substituting the expressions we found above for Ax, Bx, and Cx, we get:

-|A|cos θ + |B|sin 35.0° + |C|sin 44.0° = 0

We can also use the y-component equation to write:

Ay = |A|sin θ

By a similar process, we can write the y-component equations for vectors B and C:

By = |B|cos 35.0°
Cy = -|C|cos 44.0°

Now, using the fact that the sum of the y-components is also equal to zero, we can write:

Ay + By + Cy = 0

Substituting the expressions we found above for Ay, By, and Cy, we get:

|A|sin θ + |B|cos 35.0° - |C|cos 44.0° = 0

We now have two equations with two unknowns (|A| and |B|) and can solve for them using algebraic methods. Once the magnitudes of A and B are found, we can use the original equations to find their respective directions.