1. **Problem Statement:** A surveyor is standing 115 feet from the base of the Washington Monument. The angle of elevation to the top of the monument is 78.3°. We need to find the height of the monument. 2. **Formula Used:** In a right triangle, the tangent of an angle is the ratio of the opposite side (height of the monument) to the adjacent side (distance from the monument). So, $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ 3. **Apply the formula:** Here, $\theta = 78.3^\circ$, adjacent side = 115 ft, and opposite side = height of the monument. $$\tan(78.3^\circ) = \frac{\text{height}}{115}$$ 4. **Solve for height:** Multiply both sides by 115: $$\text{height} = 115 \times \tan(78.3^\circ)$$ 5. **Calculate the value:** Using a calculator, $$\tan(78.3^\circ) \approx 4.83$$ So, $$\text{height} = 115 \times 4.83 = 555.31 \text{ ft}$$ 6. **Answer:** The Washington Monument is approximately **555.31 feet** tall.