NICET - Highway Construction Inspection Practice Exam

What does the tangent length formula represent?

1. T = R * sin(I / 2)

2. T = R * tan(I / 2)

3. T = L / 2

4. T = 2 * πR

The correct answer is: T = R * tan(I / 2)

The tangent length formula, specifically represented as T = R * tan(I / 2), describes the length of the tangent line segment from a point on the circumference of a circle to the point of tangency. In this formula, R represents the radius of the circle, and I is the central angle in radians subtended by the arc. The tangent at a given point on the circle can be visualized as forming a right triangle with the radius and a line perpendicular to it at the tangent point. Using the tangent function relates the angle to the opposite side (the tangent length) and the adjacent side (the radius). Thus, if you know the radius and the angle, you can calculate the length of the tangent. This relationship is fundamental in geometric constructions, particularly in road design and alignment, as it helps in understanding the layout of curves and tangents in highway construction. The other options represent different relationships not directly related to the tangent length in this geometric context. One involves a sine function, which pertains more to circular segment calculations. Another option presents a simple half-length division relevant to linear dimensions but not to tangential lines, and the last option provides the circumference of the circle, which describes the entire circular path rather than a tangent. Understanding these