Solve each problem. (Modeling) Highway Curves A basic highway curve conne...

Solve each problem.

(Modeling) Highway Curves A basic highway curve connecting two straight sections of road is often circular. In the figure, the points P and S mark the beginning and end of the curve. Let Q be the point of intersection where the two straight sections of highway leading into the curve would meet if extended. The radius of the curve is R, and the central angle θ denotes how many degrees the curve turns. (Source: Mannering, F. and W. Kilareski, Principles of Highway Engineering and Traffic Analysis, Second Edition, John Wiley and Sons.)

(a) If R = 965 ft and θ = 37° , find the distance d between P and Q.

(b) Find an expression in terms of R and θ for the distance between points M and N.