Question

Two straight lines intersect at an angle of \(120^\circ\). The radius of the curve joining the straight lines is \(500m\). The length of the long chord and mid-ordinate in meters of the curve are:

• A. \(250, 33.493\)
• B. \(500, 66.987\)
• C. \(866.025, 250\)
• D. \(500, 250\)

Hint:

The long chord is calculated using \(2R \sin (\Delta/2)\) and the mid-ordinate is computed using \(R(1 - \cos(\Delta/2))\). These formulas are essential for curve geometry in surveying.

Answer 1

The Correct Option is C

Step 1: Understanding the formula for the long chord. The length of the long chord (\(L\)) for a circular curve is given by: \[ L = 2R \sin \left(\frac{\Delta} {2}  \right) \] where: - \( R \) = 500m (radius), - \( \Delta \) = \(180^\circ - 120^\circ = 60^\circ\). 
Step 2: Calculating the long chord. \[ L = 2 \times 500 \times \sin \left(30^\circ\right) = 1000 \times 0.5 = 500m. \] 
Step 3: Computing the mid-ordinate (\(M\)). The mid-ordinate is given by: \[ M = R \left( 1 - \cos \frac{\Delta}{2}  \right) \] Substituting values: \[ M = 500 \left( 1 - \cos 30^\circ \right) = 500 \times (1 - 0.866) \] \[ M = 500 \times 0.134 = 66.987m. \] 
Step 4: Selecting the correct option. Thus, the correct values are \(866.025, 250\).