1. **State the problem:** We need to find the cosecant of angle $D$ in triangle $CED$ where $CE=55$, $ED=48$, and $CD=73$. Angle $E$ is a right angle. 2. **Recall the definition:** Cosecant is the reciprocal of sine. For angle $D$, $$\csc(D) = \frac{1}{\sin(D)}.$$ 3. **Identify sides relative to angle $D$:** In right triangle $CED$, angle $E$ is $90^\circ$, so side $CE$ and $ED$ are legs, and $CD$ is the hypotenuse. 4. **Calculate $\sin(D)$:** Sine of angle $D$ is opposite over hypotenuse. The side opposite angle $D$ is $CE=55$, hypotenuse is $CD=73$. $$\sin(D) = \frac{CE}{CD} = \frac{55}{73}.$$ 5. **Calculate $\csc(D)$:** $$\csc(D) = \frac{1}{\sin(D)} = \frac{1}{\frac{55}{73}} = \frac{73}{55}.$$ 6. **Simplify the fraction:** $73$ and $55$ have no common factors other than 1, so the fraction is already simplified. **Final answer:** $$\boxed{\csc(D) = \frac{73}{55}}.$$