Between Massena and Anaheim there are two railroad tracks. One of them is straight and is 4 miles long. The other one is the arc of a circle and is 5 miles long.
What is the radius of curvature of the curved track?
From the problem, we get an arch A of length 5 whose endpoints are connected by a straight line B of length 4. Supposing O to be centre of curvature, we make an isocelles triangle whose equal sides are each of length l and the base is B=4. Let x (inradians) be the angle at O. So we get two unknowns : x and l (which is also radius ofcurvature). And we have two equations:
sin(x/2) = 2/l --->(b) [since we have an isocelles triangle]
solving, we get l which is required