Practice Question: Length of Horizontal Curve Based on Tangent and Radius

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Solution

Answer: C) 567 ft

Consider the relationships between tangent, radius, intersection angle, and length:

\[T=R\tan \frac\phi2\]
\[L= \frac{\pi\ R\ \phi}{180°}\]
Determine the intersection angle:

\[\phi=2\ \ tan^{-1} (\frac TR)\]
\[\phi=2\ \ tan^{-1}(\frac {300\ ft}{700\ ft})=46.4°\]

Solve for length based on intersection angle and radius:

\[L=\frac{\pi\ \times\ 700\ ft\ \times\ (46.4°)}{180°}=567 ft\]
 

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