Instructions:

Use only US customary units. Use appropriate code provisions in US customary units.

Show all steps and calculations. Failure to show detailed calculations will result in points deducted.

Problem $1.$

Design a horizontal curve with the following information. Initial tangent bearing $=45{30}^{\text{'}}NE.$ Final tangent bearing $=50{30}^{\text{'}}$ SE$.$ Station location of $PC=15+10.$ Design speed on the curve $=60mph.$ Maximum superelevation $=6\%.$ The design should produce the following:

$($a$)$ Length of the curve. $($b$)$ Radius of the curve. $($c$)$ Station locations of PI and PT$.($d$)$ Degree of the curve.