I'm trying to calculate angle theta using law of cosines but I am getting varying results of which none make sense to me.
A log is 10 meters long and weighs 1 ton. A 16 meter long rope is bound to each end of the log and a hook is subsequently hooked to the middle of that rope with the intention of lifting the log, so that each 'side' of the rope becomes 8 meters. The forces y and x (Don't know how to make vector signs) are equally powerful and their sum is 1 ton. The rope also has to endure the pull of x and y regardless of the direction of the pull. Find out how much weight the rope has to support.
First, let's have a look at my hand-drawn attempt to find angle theta with the law of cosines. I intend on finding angle theta so I can subsequently use that for law of sines in order to find 'side c' (pictured as 10m) using my other unit (ton). I have 0.5 ton on each side and I want to find out how many tonnes side/vector c is (the sum of vectors y and x).
I calculate angle theta to be 77° but it seems by all accounts that the 'long angle' should be more than 90°. Also ignore the sin on my picture, I meant cos and realized later that I was doing sin, so my answer is wrong because of that, I later corrected it to 77°..
Can someone please point me to my error in calculating angle theta (or if I am wrong by assuming that it should be larger than 90°) and also tell me if I am doing this problem right at all? I'm not very confident with my approach and it is likely wrong.