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.
"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.
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 Px = 48cos30o = 41.56 and Py = 48sin30o = 24. From there, I have a right angle and I know that one leg of the triagle is Q+Px and the other is Py. 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 13.3o.
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.