# Math Help - Help Please!

Suppose the track follows the curve of a circle of radius R, and central angle between the fixed point of the rail and the midpoint of the rail is $\theta$. Then S/2=R $\theta$. Similarly, $85/2=R\sin\theta$. Solving this system of equations gives you all the information you need to find X. The vertical distance D between the ground and the center of the circle is $D=R\cos\theta$ and $X=R-D$.
Say for example, the rail expanded from 85m to 90m. Then the solution to $\frac{90}{85}=\frac{\theta}{\sin\theta}$ is $\theta=33.36^\circ$. So the radius of the circle is 77.28m and the distance from the circle's center to the ground is 64.55m. Thus, the rail is sitting 12.72m off the ground. (Obviously, a realistic value of its expansion of a few millimeters will cause it to rise only a few centimeters.)