Answer & Solution
Answer: Option
C
Solution:
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
