The departure of a line in a traverse surveying is a crucial concept for understanding navigational methods. When working with the concepts of traverse, it is vital to comprehend how the departure and latitude of a line are calculated using the properties of the angles involved.

In traverse surveying, the departure of a line is defined as its horizontal projection in the east or west direction. The departure of a line is determined using the following formula:

\(Departure = Length \times \sin(\text{Reduced Bearing})\)

Let's understand each component of this equation:

1. Length: It is the actual measured distance of the line in the field.
2. Reduced Bearing: It is the angle that the line makes with respect to the north or south, and its value ranges between 0° and 90°.
3. Sine Function: In trigonometry, the sine of an angle in a right-angled triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. For calculating departure, we use the sine of the reduced bearing.

To verify why sine is used:

• If the line is aligned perfectly with the east or west direction, the angle of the bearing is either 0° or 180°, and the sine of these angles determines the contribution of the length to the departure.
• Because sine of 0° is 0, there is no contribution in the east-west direction if the line is aligned perfectly north or south.

Based on this understanding, the correct answer is Sine. Departure is obtained by multiplying the length of the line by the sine of its reduced bearing, which accurately captures the east-west component of the line.

Conclusion: For calculating the departure of a line, use the formula: \(Departure = Length \times \sin(\text{Reduced Bearing})\). This concludes that the option Sine is the correct answer.