(Solved): 33. Circular Railroad Curves In the United States, circular railroad curves are designated by t ...

33. Circular Railroad Curves In the United States, circular railroad curves are designated by the degree of curvature, the central angle subtended by a chord of \( 100 \mathrm{ft} \). Suppose a portion of track has curvature \( 42.0^{\circ} \). (Source: Hay, W., Railroad Engineering, John Wiley and Sons.) (a) What is the radius of the curve? (b) What is the length of the arc determined by the 100 -ft chord? (c) What is the area of the portion of the circle bounded by the arc and the 100-ft chord? 135. Area of a Lot \( \mathrm{A} \) frequent problem in surveying city lots and rural lands adjacent to curves of highways and railways is that of finding the area when one or more of the boundary lines is the arc of a circle. Find the area (to two significant digits) of the lot shown in the figure. (Source: Anderson, J. and E. Michael, Introduction to Surveying, McGraw-Hill.)