Rail turn

The curve radius on a railway line is 532 m. The length of the rail track along this curve is 818 m. What is the angle ASB in degrees, where A and B are the endpoints of the curve and S is the centre of the arc?

Final Answer:

ASB =  106.7 °

Step-by-step explanation:

$$\begin{gathered} R=571\text{km} \\ l=1063\text{km} \\ l=\alpha \cdot R \\ \alpha =\frac{l}{R}=\frac{1063}{571}\doteq 1.8616\text{rad} \\ ASB=\angle ASB=\alpha \to \text{°}=\alpha \cdot \frac{180}{\pi }\text{°}=1.8616\cdot \frac{180}{\pi }\text{°}=106.7\text{°}=106.7^{\circ }=106°39^{\prime }52" \end{gathered}$$

Try another example