To find the length of \( LF \), we can use the relationship between a radius and a tangent to a circle. The radius drawn to the point of tangency is perpendicular to the tangent line.
Given:
- \( KM \) and \( KL \) are tangent to the circle at points \( L \) and \( M \) respectively.
- \( \angle LFK = 23^\circ \)
- \( KM = 47 \) feet
Since \( LAP \) (the radius to point L) is perpendicular to \( KL \) (the tangent line), we know that \( \triangle LFK \) is a right triangle with:
- \( \angle LKF = 90^\circ - \angle LFK = 90^\circ - 23^\circ = 67^\circ \).
Using the tangent ratio (opposite/adjacent):
\[ \tan(\angle LFK) = \frac{LF}{KL} \]
Substituting the known values:
\[ \tan(23^\circ) = \frac{LF}{47} \]
Now, solving for \( LF \):
\[ LF = 47 \cdot \tan(23^\circ) \]
Calculating \( \tan(23^\circ) \):
\[ \tan(23^\circ) \approx 0.4245 \]
Now plug this value back into the equation:
\[ LF \approx 47 \cdot 0.4245 \approx 19.97 \text{ feet} \]
Rounding this to the nearest foot gives \( LF \approx 20 \) feet.
Thus, the correct response is:
20 ft.