CST Survey Calculations & Coordinate Systems 2

Question 1

A traverse course has a bearing of N 30°00' E and a length of 200.00 ft. What is its latitude?

Accepted Answer

+173.21 ft

Answer

Latitude = distance × cos(bearing) = 200 × cos 30° = 173.21 ft, positive because it runs north.

Question 2

What is the departure of a course bearing S 45°00' W with a length of 100.00 ft?

Accepted Answer

-70.71 ft

Answer

Departure = 100 × sin 45° = 70.71 ft, negative because the course runs west.

Question 3

A closed traverse has a latitude misclosure of 0.30 ft and a departure misclosure of 0.40 ft. What is the linear error of closure?

Accepted Answer

0.50 ft

Answer

Linear error = √(0.30² + 0.40²) = 0.50 ft.

Question 4

A traverse with a perimeter of 5,000 ft has a linear error of closure of 0.50 ft. What is its relative precision?

Accepted Answer

1:10,000

Answer

Relative precision = 0.50 / 5,000 = 1/10,000.

Question 5

Under the compass (Bowditch) rule, how is the latitude correction for each course found?

Accepted Answer

In proportion to the course length divided by the total perimeter

Answer

The compass rule spreads the misclosure in proportion to each course's length relative to the total traverse length.

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