To solve for the length of MF, we can apply some trigonometry based on the given angle measures.
Since \(\angle L \cong \angle M = 90^\circ\), that indicates we have a right triangle. We also know that \(\angle LKF = 35^\circ\) and the length of \(KF = 12\) mm.
Using the sine function to find the length of side \(MF\) in triangle \(LKF\):
\[ \sin(\angle LKF) = \frac{opposite}{hypotenuse} \]
In this case, the side opposite to \(\angle LKF\) is \(MF\), and the hypotenuse is \(KF\). Thus we can write:
\[ \sin(35^\circ) = \frac{MF}{12} \]
Now we can rearrange this equation to solve for \(MF\):
\[ MF = 12 \cdot \sin(35^\circ) \]
Calculating \(\sin(35^\circ)\):
\[ \sin(35^\circ) \approx 0.5736 \]
Now plug this value back into the equation:
\[ MF = 12 \cdot 0.5736 \approx 6.8832 \]
To the nearest millimeter, \(MF\) is approximately 7 mm.
Therefore, the correct response is: 7 mm
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