I do not understand how to set up the following problem:
"Forces of 20 lb and 32 lb make an angle of 52 degrees with each other. find the magnitude of the resultant force."
An actually picture would really help.
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Use cosine law with an angle of 127 degrees
Here is a way using simple trigonometry, which I teach to my 12th grade Physics class.
In the diagram, your vectors are $OD$ of length $20$ and $OB$ of length $30$. To add the vectors, we "slide" a copy of $OD$ so it starts at $B$, giving us vector $BE$. We can use sine and cosine in the resulting right triangle $BEF$ to get its sides. You want vector $OE$, and you now know the sides: $EF$ which you already found, and $OF$ which equals $OB+BF$.
You can now use the Pythagorean theorem to find the length of $OE$, which is your answer.
This method uses more steps but is easier to understand than the Law of Cosines. It often also gives better precision, which is useful in Physics class.