Chapter 5 - Relationships Within Triangles - 5-2 Perpendicular and Angle Bisectors - Practice and Problem-Solving Exercises - Page 296: 12

The distance from $L$ to ray $HF$ is $27$.

The angle bisector theorem states that a point that is located on an angle's bisector is equidistant from the angle's sides. In this diagram, we see that the ray $HL$ is the angle bisector of $\angle KHF$. Therefore, $L$, which is a point on the bisector, is equidistant from the sides of the angle. So, $L$ is equidistant from ray $HK$ and ray $HF$. If the distance from $L$ to ray $HK$ is $27$, then the distance from $L$ to ray $HF$ is also $27$.