1. **Problem Statement:** Find the secant of angle $E$ in right triangle $FDE$ where $\angle F$ is the right angle. The sides are given as $FD = 2\sqrt{3}$ (adjacent to $E$), $ED = 4$ (hypotenuse), and $FE$ (opposite to $E$) is unknown. 2. **Formula:** The secant of an angle in a right triangle is defined as the ratio of the hypotenuse to the adjacent side: $$\sec(E) = \frac{\text{hypotenuse}}{\text{adjacent side}}$$ 3. **Identify sides relative to $\angle E$:** - Hypotenuse $ED = 4$ - Adjacent side to $E$ is $FD = 2\sqrt{3}$ 4. **Calculate $\sec(E)$:** $$\sec(E) = \frac{4}{2\sqrt{3}}$$ 5. **Simplify the fraction:** $$\sec(E) = \frac{\cancel{4}}{\cancel{2}\sqrt{3}} = \frac{2}{\sqrt{3}}$$ 6. **Rationalize the denominator:** $$\sec(E) = \frac{2}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{2\sqrt{3}}{3}$$ 7. **Final answer:** $$\boxed{\sec(E) = \frac{2\sqrt{3}}{3}}$$