# Surveying Questions and Answers – Theodolite Traversing – Computation of Latitude and Departure

This set of Surveying Multiple Choice Questions & Answers (MCQs) focuses on “Theodolite Traversing – Computation of Latitude and Departure”.

1. Departure refers to __________
a) Co-ordinate length measured at right angles
b) Co-ordinate length measured at right angles to the meridian direction
c) Co-ordinate length measured parallel to the assumed meridian direction
d) Co-ordinate length measured parallel to the datum

Explanation: Departure is the Co-ordinate length measured at right angles to the meridian direction and latitude refers to the Co-ordinate length measured parallel to assume meridian direction.

2. When measured towards southward, latitude is negative.
a) True
b) False

Explanation: Depending on the quadrant in which it lies, the latitude and departure were given signs. For latitude, it is taken as positive in north and negative towards south direction. Similarly, departure is positive when taken in east direction and negative when taken in west direction.

3. Departure can be given as __________
a) D = l cos θ
b) D = l tan θ
c) D = l cosec θ
d) D = l sin θ

Explanation: The formula for departure can be given as D = l sin θ and for latitude it is given as L = l cos θ. Where, l refers to length of line.

4. Consecutive co-ordinates are also known as __________
a) Total co-ordinates
b) Independent co-ordinates
c) Dependent co-ordinates
d) Departure co-ordinates

Explanation: Latitude and departure co-ordinates of any point with reference to the preceding point are equal to the latitude and departure of the line joining the preceding point to the point under consideration. Such co-ordinates are known as consecutive co-ordinates or dependent co-ordinates.

5. Latitude and Departure equations will never return positive values.
a) False
b) True

Explanation: Because a bearing angle never exceeds 90°, the Latitude and Departure equations will return positive values.
Sin (0°) to Sin (90°) ranges from 0 to 1
Cos (0°) to Cos (90°) ranges from 1 to 0
The correct mathematical sign for the Latitude and Departure come from the bearing quadrant.
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6. For calculating latitude and departure they must be converted into__________
a) Whole Circle Bearing system
b) Reduced Bearing system
c) True bearing system
d) Assumed bearing system

Explanation: For calculating the latitudes and departure of the traverse lines, it is essential to reduce the bearing in the Quadrantal or reduced bearing system.

7. The latitude for the figure can be given as __________(θ = 500 34ꞌ)

a) 160.43m
b) 151.34m
c) 161.34m
d) 165m

Explanation: We know that, latitude of side can be determined by the formula L = l cos θ. So, on substitution we get,
L = l cos θ = 245* cos (500 34ꞌ) = 161.34m.

8. S-W lies in which of the following quadrant______________

a) IV
b) II
c) I
d) III

Explanation: From the figure it is clear that S-W lies in the Third quadrant when taken in clockwise direction.

9. By which of the following step, Independent co-ordinate can be obtained?
a) ∑L + ∑D
b) ∑L – ∑D
c) ∑L2 + ∑D2
d) ∑L2 – ∑D2

Explanation: The total latitude and departure of any point with respect to a common origin is known as independent co-ordinate. The independent co-ordinates of any point may be obtained by adding algebraically the latitudes and the departure of the lines between the point and origin.

10. Total co-ordinate point is referred as___________
a) Dependent co-ordinate point
b) Independent co-ordinate point
c) Consecutive co-ordinate point
d) Departure co-ordinate point

Explanation: The total latitude and departure of any point with respect to a common origin is known as independent co-ordinates or total co-ordinate of the point.

11. If the value of θ = 720 49ꞌ, find the value of departure for side having a length 300 m.
a) 286.17
b) 268.91
c) 286.61
d) 286.16

Explanation: We know that the value of departure can be given as D = l sin θ. On substitution of the values of θ and l we get,
D = 300 * sin (720 49ꞌ) = 286.61 m.

12. The value of θ = 1620 49ꞌ in Reduced Bearing system can be represented as ____________
a) S1706ꞌE
b) S27026ꞌE
c) S7026ꞌE
d) S17026ꞌE

Explanation: Any angle in Whole Circle Bearing system can be transformed into reduced bearing system by using a relation, it can be given as
R.B = 1800 – W.C.B which means R.B = 1800 – 162024ꞌ = 17026ꞌ = S17026ꞌE.
In R.B system, the direction of the angle is also mentioned along with the value.

13. What will be the value of total co-ordinate of B, if it is initially assumed as 100 and N latitude at A is given as 192.96?
a) 292.96
b) 92.96
c) 229.69
d) 29.69

Explanation: The value of total co-ordinate can be given by adding the assumed value to the previously mentioned value i.e.
Total co-ordinate + latitude at A = 100 + 192.96 = 292.96
The total co-ordinate at B is given as 292.96.

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