1. The problem statement, all variables and given/known data So we have a force of unknown magnitude acting on these struts at an angle θ measured from strut AB. The component of the force acting along AB is 600lb, and the magnitude of the force acting along BC is 500lb. If Φ = 60°, what is the magnitude of F and the angle θ? 2. Relevant equations Fcos(θ) = 600lb 3. The attempt at a solution Ok. So, it'll probably help if I knew the third angle of the triangle formed. 180° = ɣ + (60° + 45°) 180° - 105° = ɣ 75° = ɣ Great. So, I know that Fcos(θ) = 600lb, and Fcos(75° - θ) = 500lb hm. Fcos(θ)/600 = 1 = Fcos(75 - θ)/500 500Fcos(θ) = 600Fcos(75° - θ) 5Fcos(θ) = 6Fcos(75° - θ) 5cos(θ) = 6cos(75° - θ) 0 = 5cos(θ) - 6cos(75° - θ) Originally I tried finding where z = 5cos(θ) - 6cos(75° - θ) intersected with z = θ + η where η = 75° + θ, but I couldn't get Wolfram Alpha to understand what I was talking about. Here, I see I should have just left η as 75° - θ, but even still, I have to *ask* Wolfram Alpha what θ works for 0 = 5cos(θ) - 6cos(75° - θ) when 0<=θ<=75° (it gives me an angle of ~30.7°). Worse, since I couldn't figure it out, I figures if I gave in on the magnitude of F, I could still find the angle. Mastering Engineering told me F = 870lb. So, if Fcos(θ) = 600, θ=arccos(600/F) and arccos(600/870) ≈ 46.4°. Which was wrong. The θ it wanted was ~34° Which means everything I did was wrong. So what triangle magic do I do to get from the initial problem, to the final F=870 θ=34°, without doing something so complicated I need Wolfram Alpha to crunch it out?