In general, the length of a tangent to a simple curve cannot be directly found by just subtracting the vertex from the stationing of the Point of Curvature (PC). Here's why:

1. Vertex: The vertex of a curve is the point where the curve changes direction, which is typically the center of the circular arc for a simple curve.
2. Stationing of PC (Point of Curvature): The stationing of the PC is the position of the point where the curve begins to deviate from a straight path, or the point where the circular arc starts.

Formula for Tangent Length

The length of the tangent (denoted as $T$) is related to the radius $R$ of the curve and the central angle $\Delta$. It can be calculated using the following formula:

$T = R \cdot \tan \left( \frac{\Delta}{2} \right)$

Where:

• $T$ is the tangent length.
• $R$ is the radius of the curve.
• $\Delta$ is the central angle.

The relationship between the radius, the central angle, and the position of the PC is important here, but simply subtracting the vertex position from the stationing of the PC doesn’t provide enough information to calculate the length of the tangent.

Correct Approach

To find the length of the tangent from a simple curve, you would typically:

• Know the radius $R$ and central angle $\Delta$ (or other geometric parameters of the curve).
• Use the appropriate tangent length formula or geometric principles to solve.

If you have the stationing of the PC and know the radius, I can help you calculate the length of the tangent using the correct method.

Would you like to work through an example or need further clarification on this?