1. **State the problem:** We need to find the height $h$ of the Washington Monument given the angle of elevation $78^\circ$ and the distance from the base $118$ ft. 2. **Identify the right triangle sides:** The height $h$ is the side opposite the angle $78^\circ$, and the base adjacent to the angle is $118$ ft. 3. **Use the tangent function:** In a right triangle, $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. 4. **Set up the equation:** $$\tan(78^\circ) = \frac{h}{118}$$ 5. **Solve for $h$:** $$h = 118 \times \tan(78^\circ)$$ 6. **Calculate $\tan(78^\circ)$:** Using a calculator, $\tan(78^\circ) \approx 4.70463$. 7. **Find $h$:** $$h = 118 \times 4.70463 = 555.146$$ 8. **Final answer:** The height of the Washington Monument is about $555$ ft.