How to find the values of the following forces when it isn't given?

I think you just express the moment at A in terms of F_{n}.

Assuming counterclockwise moment as positive: $M_A = 4\left( \frac{3}{5}F_1 \right) - 5\left( \frac{4}{5}F_1 \right) - 1(F_2) + 5\left( \frac{5}{13}F_3 \right) + 2\left( \frac{12}{13}F_3 \right)$

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I think you just express the moment at

Ain terms ofF._{n}Assuming counterclockwise moment as positive:

$M_A = 4\left( \frac{3}{5}F_1 \right) - 5\left( \frac{4}{5}F_1 \right) - 1(F_2) + 5\left( \frac{5}{13}F_3 \right) + 2\left( \frac{12}{13}F_3 \right)$