Static Equilibrium: Proving Forces are Equal

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In static equilibrium, three forces acting on an object must balance, resulting in a net force of zero. To prove that the forces are equal, one can represent them as vectors forming a triangle, where each force corresponds to a side of the triangle. The relationship between the forces can be established using the sine of the angles between them. By applying trigonometric principles, it can be shown that the ratio of each force to the sine of its corresponding angle is equal. This geometric representation confirms that the forces are indeed in equilibrium.
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Three forces act on an object in static equilibrium.
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(a) If F1 and F2 represent the magnitudes of the forces acting on the object, show that
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.

(b) Show that
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I know that the sum of all forces needs to be zero if the system is in equilibrium, but I don't know how to prove that each force divided by the sine of theta is equal to each other.
 
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when you add three forces (in representation ) which are in equilibrium, you get a triangle
this is because the net magnitude is zero. Draw such a diagram and then solve the question
 
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