Question Details

The Whole Circle Bearing (WCB) of line AB is 150◦. The length of AB is 100 m. The latitude and departure values, respectively, for this line are:

Options

A

+86.60 ; +50.00

B

+86.60 ;-50.00

C

-86.60 ; +50.00

D

-86.60 ;-50.00

Show Answer

Correct Answer :

Option C

-86.60 ; +50.00

Solution :

To find the latitude and departure of line AB, we use the standard surveying definitions for these coordinates.

The latitude (L) of a line is its projection on the North-South meridian. It is calculated as:
L=lcos(θ)
where:
- l is the length of the line.
- θ is the Whole Circle Bearing (WCB) of the line.

The departure (D) of a line is its projection on the East-West parallel. It is calculated as:
D=lsin(θ)

Given data:
- Length of the line (l) = 100 m
- Whole Circle Bearing (θ) = 150°

Now, let's compute the latitude:
L=100cos(150°)

Since cos(150°)=-cos(30°)=-0.866025, we have:
L=100×(-0.866025)=-86.60 m

Next, let's compute the departure:
D=100sin(150°)

Since sin(150°)=sin(30°)=0.5000, we have:
D=100×0.5000=+50.00 m

Therefore, the latitude is -86.60 and the departure is +50.00.

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