1. **Problem:** Determine the measure of angle $\angle L$ in the right triangle with vertices $F, L, H$, where $\angle F$ is the right angle, $FL = 2.5$ cm, $FH = 3.7$ cm, and $\angle HFL = 34^\circ$. 2. **Formula and rules:** In a right triangle, the sum of the angles is $180^\circ$. Since $\angle F = 90^\circ$, the other two angles must add to $90^\circ$. So, $$\angle L = 90^\circ - \angle HFL$$ 3. **Calculation:** $$\angle L = 90^\circ - 34^\circ = 56^\circ$$ 4. **Answer:** The measure of angle $\angle L$ is $56^\circ$. This corresponds to choice D.