1. **Problem Statement:** We are given a spiral curve with two tangents intersecting at an angle of 108.2° at station STA 16+610. The radius of the central curve is 123.19 m, and the length of the spiral curve is 139.89 m. We need to find the station of the end of the central curve. 2. **Relevant Formulas and Concepts:** - The deflection angle $\Delta$ between the tangents is given as 108.2°. - The length of the spiral curve $L_s = 139.89$ m. - The radius of the central curve $R = 123.19$ m. - The length of the central curve $L_c$ can be found using the formula: $$L_c = R \times (\Delta - 2 \times \theta_s)$$ where $\theta_s$ is the spiral angle. - The spiral angle $\theta_s$ is calculated by: $$\theta_s = \frac{L_s}{2R}$$ - The station of the end of the central curve is the station at the intersection minus the length of the spiral curve and the length of the central curve: $$STA_{end} = STA_{intersection} - L_s - L_c$$ 3. **Calculate the spiral angle $\theta_s$:** $$\theta_s = \frac{139.89}{2 \times 123.19} = \frac{139.89}{246.38} = 0.5677 \text{ radians}$$ Convert to degrees: $$0.5677 \times \frac{180}{\pi} = 32.53^\circ$$ 4. **Calculate the central curve deflection angle:** $$\Delta - 2 \times \theta_s = 108.2^\circ - 2 \times 32.53^\circ = 108.2^\circ - 65.06^\circ = 43.14^\circ$$ Convert to radians: $$43.14^\circ \times \frac{\pi}{180} = 0.7533 \text{ radians}$$ 5. **Calculate the length of the central curve $L_c$:** $$L_c = R \times (\Delta - 2 \times \theta_s) = 123.19 \times 0.7533 = 92.81 \text{ m}$$ 6. **Calculate the station of the end of the central curve:** Convert STA 16+610 to meters: $$16 \times 100 + 610 = 1610 \text{ m}$$ Subtract the spiral length and central curve length: $$STA_{end} = 1610 - 139.89 - 92.81 = 1610 - 232.7 = 1377.3 \text{ m}$$ 7. **Final answer:** The station of the end of the central curve is $\boxed{1377.300}$ (rounded to 3 decimal places).