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Now, with the green line, you can see two triangles. right? Also, you know where the point between 2 and 3 (let us call it D) is located, because you know how long 3 is and can tell the angle in A (the corner where 3 touches the mirror) by the animation state.
Now, you need to know the other triangle: length of arm 1 is known. length of 2 is known. length of the diagonal (BD) is known. But the three angles are unknown.
And we know as well: There can be only ONE triangle with the same kind of lengths at its three sides. The angles are also already defined. That is what I meant to show with the circles.
This is where the law of sines gets into play: with it, you can find the relations between the angles and actually can find a solution for the triangle. Together with the angle between green line(BD) and mirror (AB) you can then calculate all animation angles.
Now, you need to know the other triangle: length of arm 1 is known. length of 2 is known. length of the diagonal (BD) is known. But the three angles are unknown.
And we know as well: There can be only ONE triangle with the same kind of lengths at its three sides. The angles are also already defined. That is what I meant to show with the circles.
This is where the law of sines gets into play: with it, you can find the relations between the angles and actually can find a solution for the triangle. Together with the angle between green line(BD) and mirror (AB) you can then calculate all animation angles.