In the first sample problem, the given quantities are the radius, the angle of intersection, and some distance from the PC. The first thing I did is find the angle that the distance made with the center of circle. Then, using the formula to find the length of curve, I derived a formula to find the theta or the angle. For instance, the angle that I got is 10° 34' 34.21''. Lastly, using the formula for the middle ordinate, I was able to find the x which is 3.367m.
For the second problem, the given quantities are the angle of intersection and the external distance. In this problem, I simply used the external distance formula to derive the formula for radius. A lot of algebraic manipulations happened before I arrive to the final answer of 226.942m radius.
Just like the computation for missing data, the problems involving vertical curves also need sketch or drawing to visualize the missing quantities in the curve. Further, one should familiarize the different parts of the curve and their formulas to easily solve a problem involving curves. Though there are three more kinds of horizontal curve namely, compound, reverse, and spiral, our instructor was able to discuss up to the simple curve because of the limited time.