Finding magnitude and direction of vectors help

AI Thread Summary
To find the magnitude and direction of vector C in the equation 2A + C - B = 38 lb in the +x direction, the x and y components of vectors A and B must first be calculated using trigonometric functions. The horizontal and vertical components are derived from the angles given for each vector. After determining these components, the next step involves setting up equations based on the resultant vector's conditions. The discussion highlights the need for clarity on how to manipulate these components to isolate and solve for vector C. This problem emphasizes the application of vector addition and the importance of understanding vector components in physics.
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Homework Statement



Given the following force vectors: A is 27 lb at an angle of 28° clockwise from the +x-axis, and B is 44 lb at an angle of 52° clockwise from the +y-axis.
(a) Using the method of components find the magnitude and angle of the vector C such that 2A + C − B results in a vector with a magnitude of 38 lb pointing in the +x direction.

Homework Equations


Horizontal component of a Vector A = A * cos \Phi
Vertical Component of a Vector A = A* sin \Phi
tan \Phi = Vertical component of A/horizontal component of A
Pythagorean Theorem

The Attempt at a Solution


To solve this, I've calculated the x and y components of vectors A and B, but do not know where to go from here. The closest I could get to an answer was I drew the vectors in coordinate system and drew the resultant vector that was asked of me. But I have no idea how to proceed with finding the magnitude and the exact direction.
A, B, and C are vectors.
Thanks for explaining.
 
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Thanks, that helped.
 
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