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## Homework Statement

Two forces

**P**and

**Q**are applied to the lid of a storage bin as shown (see picture). Knowing that P = 48N and Q = 60N, determine by trigonometry the magnitude and direction of the resultant of the two forces.

## Homework Equations

"The triangle method" where you put each vector tip-to-tail, and then use components of one vector to make a right triangle (see picture).

Also, law of sines, law of cosines (??), and sin, cos, tan.

Pythagorean Thm

## The Attempt at a Solution

As you can see, I turned the picture somewhat sideways so that Q lays flat.

I used simple trig to find P

_{x}= 48cos30

^{o}= 41.56 and P

_{y}= 48sin30

^{o}= 24. From there, I have a right angle and I know that one leg of the triagle is Q+P

_{x}and the other is P

_{y}. Using Pythagorean theorem, I got 104N, which is the right magnitude for the resultant.

My problem is the angle of the resultant. When I solve for the angle θ (between Q and R) in my picture, I get 13.3.

I used tanθ = 24/101.56

as well as the law of sines (104/sin150) = (48/sinθ)

both yield the 13.3

^{o}.

Even adding 13.3 to the 25 degree angle lid and past the 55 degree Q vector, I still don't get the right answer (which is 86.7 degrees, with an angle symbol pointing into the second quadrant, not sure what that means either).

Thanks for any help.