The minimum distance of each point is $A$, and I don't know how to calculate the length of $b$, the solution said
$b^2=a^2+A^2-2aAcos(75)$,but i don't understand the reason about this formula, can anyone help me?

The minimum distance of each point is $A$, and I don't know how to calculate the length of $b$, the solution said
$b^2=a^2+A^2-2aAcos(75)$,but i don't understand the reason about this formula, can anyone help me?

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You should use the cosine rule. In this case it tells you: $$b^2=a^2+A^2-2aAcos(\alpha).$$
We're looking at the following triangle:
Now you only need to find the angle, and you're done.