Track arc

Two straight railway tracks meet at an angle of 126°. They are joined by a circular arc with radius r = 1110 m. How long is the connecting arc (L)? How far is the centre of the arc from the intersection of the tracks (x)?

Final Answer:

L =  1046.2 m
x =  1245.8 m

Step-by-step explanation:

$$\begin{gathered} \alpha =126{}^{\circ } \\ r=1110\text{m} \\ \beta =180-\alpha =180-126=54{}^{\circ } \\ B=\beta =54°=0.94248=3\pi /10 \\ L=r\cdot B=1110\cdot 0.9425=1046.2\text{m} \end{gathered}$$

$$\begin{gathered} \gamma =\alpha /2=126/2=63{}^{\circ } \\ x=\frac{r}{\sin \gamma }=\frac{r}{\sin 63°}=\frac{1110}{\sin 63°}=\frac{1110}{0.891007}=1245.8=1245.8\text{m} \end{gathered}$$

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