Question

Road A and Road B are joined by a circular horizontal curve of radius 200 m as shown in the figure. Road A and Road B are tangential to the curve at the points C and D, respectively. Had the curve not been there, straight roads A and B would have met at the point E. The distance from C to E is 92 m. The value of angle \( \theta \) (in degrees) is ........... (rounded off to 1 decimal place).

• A. 49.40°
• B. 48.50°
• C. 50.00°
• D. 45.30°

Hint:

In circular curve problems, remember that the tangent length and the angle \( \theta \) are related through trigonometric formulas involving the radius and the distances between the tangents.

Answer 1

The Correct Option is A

The tangent length \( CE \) can be calculated using the formula: \[ CE = R \cdot \tan \left(\frac{\theta}{2}\right), \] where \( R = 200 \, {m} \) (radius of the curve) and \( CE = 92 \, {m} \) (distance from C to E). Rearranging the formula, we get: \[ \theta = 2 \cdot \tan^{-1} \left( \frac{92}{200} \right). \] Calculating the value: \[ \theta = 2 \cdot \tan^{-1} \left( 0.46 \right) \approx 49.40^\circ. \] Thus, the value of angle \( \theta \) is approximately 49.40°, which corresponds to option (A).