A horizontal curve is characterized by its radius, intersection angle, and stationing of key points. In this case, the radius is 400 meters, and the angle of intersection is 30 degrees, with the station of the point of curvature (P.C.) at 0 + 150 meters. The goal is to determine the station values at the point of intersection (P.I.), point of tangency (P.T.), and midpoint of the curve, as well as the length of the long chord.

The process begins with calculating the tangent distance (T) and the length of the curve (L). The tangent distance depends on the radius and the tangent of half the intersection angle. The curve length depends on the radius and the intersection angle converted to radians.

The station of the P.I. is found by adding the tangent distance to the station of P.C., and the station of P.T. is determined by adding the curve length to the station of P.C. The station of the midpoint of the curve is calculated by adding half the curve's length to the station of P.C.

The length of the long chord, which spans the curve directly between the P.C. and P.T., is derived using trigonometric relationships involving the radius and intersection angle. These calculations ensure precise stationing and design integrity in setting out simple horizontal curves.