drnoisewater1
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Homework Statement
Two forces P and Q with respective magnitudes 100N and 200N are applied to the upper corner of a crate. The sum of the two forces is to the right (+x direction) with a magnitude of 250N. Find the angles that P and Q make with their sum - that is, with the horizontal line through +x axis.
Homework Equations
R = P + Q where R is the resultant vector and P and Q are vectors given in the problem
Rx = Px + Qx = 250
Ry = Py + Qy = 0
The Attempt at a Solution
All the information is given except the two angles. Plugging in the given values gives me the equation:
\SigmaRx = 100cos(\theta) + 200cos(\phi) = 250N
\SigmaRy = 100sin(\theta) - 200sin(\phi) = 0
where theta is the angle between P and R and phi is the angle between Q and R.
Basically this comes down to confusion on algebra for me. I attempted substitution and that got me nowhere. I know there is some kind of trick to solving this, but I cannot figure it out. There are two equations and two unknowns so there must be a way to do it. I have worked a similar problem where one of the angles is known and the other was supposed to be at a maximum and calculus could be used there. Is that a possibility in this problem or is there just a little trick that I am missing?