1. **Problem Statement:** Find the cosecant of angle $C$ in the right triangle $CDB$ where $\angle D$ is the right angle. 2. **Given:** - Side $CD = 4\sqrt{66}$ - Side $DB = 4\sqrt{22}$ - Hypotenuse $CB = 8\sqrt{22}$ 3. **Recall the definition:** $$\csc(C) = \frac{1}{\sin(C)} = \frac{\text{hypotenuse}}{\text{opposite side to } C}$$ 4. **Identify sides relative to $\angle C$:** - Opposite side to $C$ is $DB = 4\sqrt{22}$ - Hypotenuse is $CB = 8\sqrt{22}$ 5. **Calculate $\csc(C)$:** $$\csc(C) = \frac{CB}{DB} = \frac{8\sqrt{22}}{4\sqrt{22}}$$ 6. **Simplify the fraction:** $$\csc(C) = \frac{\cancel{8}\times\sqrt{22}}{\cancel{4}\times\sqrt{22}} = \frac{2}{1} = 2$$ 7. **Final answer:** $$\boxed{2}$$