If the reduced bearing of a line AB is N 60° W and length is 100 m, then the latitude and departure respectively of the line AB will be

Solution (By Examveda Team)

Understanding Reduced Bearing: The reduced bearing of a line gives its direction with respect to the North-South line. N 60° W means the line is 60° to the West of North, placing it in the North-West (NW) quadrant.

Key Concept: To find the components of the line, we break it into:

1. Latitude – This is the North-South component.
2. Departure – This is the East-West component.

Signs:
Latitude is positive (+) if the line goes North, negative (-) if South.
Departure is positive (+) if the line goes East, negative (-) if West.

Formulas:
Latitude = Length × cos(angle)
Departure = Length × sin(angle)

Given:
Length = 100 m
Bearing = N 60° W (angle = 60°)

Step 1: Calculate Latitude
Latitude = 100 × cos(60°) = 100 × 0.5 = +50 m (positive because direction is North)

Step 2: Calculate Departure
Departure = 100 × sin(60°) = 100 × 0.866 = 86.6 m
Since the direction is West, it is negative: -86.6 m

Final Answer:
Latitude = +50 m
Departure = -86.6 m

Correct Answer: Option C: +50 m, -86.6 m