Join 60,000+ competitive exam aspirants
or with email
Your Cart
Subtotal₹0
Total₹0
Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
Join 60,000+ competitive exam aspirants
In a closed traverse where we were observed that it has total latitude -100m and departure 50m so calculate closing error and angle of closure.
A) e=111.80 m, θ=26.56°
B) e=111.80 m, θ=S26.56°E
C) both A and B
D) None of the above
e=111.80 m, θ=S26.56°E
Given: Total Latitude (∑L) = −100 m, Total Departure (∑D) = 50 m
Total Latitude (∑L) = −100 m, Total Departure (∑D) = 50 m
e=(∑L)2+(∑D)2,tanθ=∑L∑D
Calculate Closing Error (e)
The closing error e is the magnitude of the resultant error, calculated using the square root of the sum of squares of total latitude and total departure.
e=(−100)2+(50)2=10000+2500=12500≈111.80 m
Calculate Angle of Closure (θ)
The reduced bearing angle θ is given by the tangent of the absolute ratio of total departure to total latitude.
tanθ=∑L∑D=−10050=0.5⟹θ=tan−1(0.5)=26.565°≈26.56°
Determine Quadrant and Reduced Bearing
Since total latitude ∑L is negative (South) and total departure ∑D is positive (East), the closing error vector lies in the South-East quadrant (4th quadrant). Therefore, the direction is expressed as S26.56°E.
Bearing of closure=S26.56°E
B is correct because the magnitude of the closing error is 111.80 m and its direction in Quadrantal Bearing notation is S26.56°E due to negative latitude and positive departure.
If total latitude is zero and total departure is non-zero, the closing error lies along the East-West axis. Bowditch's (Compass) rule is commonly applied to distribute closing errors proportionally to side lengths.