Why Do Sines and Cosines Appear in Calculating the Sum of Torques?

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Hi.

I am working on this problem, which I have uploaded as a picture.
I have a question to the sum of torques.

Is there somebody how can explain me where all the sines and cosines comes from.
I am not so good to the find sum of torques.
 

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Well, first start by calculating the individual torques.
 
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