A closed traverse has ΣLatitudes = +0.084 m and ΣDepartures = −0.112 m over a total length of 1,240 m. Find the linear misclosure and the precision.

Start with the thinking

• Misclosure is the vector sum of the two errors.
• Precision is expressed as 1 in N.

Step-by-step solution

1. Misclosure

   $$e = \sqrt(0.084^{2} + 0.112^{2}) = \sqrt(0.00706 + 0.01254)$$

2. Evaluate

   $$e = \sqrt0.01960 = 0.140 m$$

3. Precision

   $$P = e/perimeter = 0.140/1,240 = 1.13\times10^{-4}$$

4. Express

   $$1 : 1/1.13\times10^{-4} = 1 : 8,860$$

Why the other options are there

• e = 0.196 m (errors added directly)
• 1:1,240 (perimeter reported as precision)

Reference: FE Reference Handbook — Surveying — Traverse computations

A surveying problem uses Traverse latitude. Given course length (L) = 438.0 ft; bearing angle (theta) = 38.0000 deg, determine the latitude (Lat) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Traverse latitude.
• Everything except Lat is given, so isolate Lat symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Surveying items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Lat = L \cos(\theta)$$

2. Step 2 — Rearrange the relation so that Lat stands alone on the left-hand side.

3. Step 3

   $$List the givens: course length (L) = 438.0 ft, bearing angle (theta) = 38.0000 deg$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$Lat = 345.1\ \text{ft}$$

6. Step 6 — Check: returning Lat = 345.1 ft to

   $$Lat = L \cos(\theta)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 690.3 — kept a factor of two that cancels in the correct rearrangement.
• 172.6 — dropped that same factor in the other direction.
• 379.7 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Surveying → Latitudes and Departures

A surveying problem uses Traverse latitude. Given bearing angle (theta) = 6.0000 deg; latitude (Lat) = 697.9 ft, determine the course length (L) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Traverse latitude.
• Everything except L is given, so isolate L symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Surveying items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Lat = L \cos(\theta)$$

2. Step 2 — Rearrange the relation so that L stands alone on the left-hand side.

3. Step 3

   $$List the givens: bearing angle (theta) = 6.0000 deg, latitude (Lat) = 697.9 ft$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$L = 701.7\ \text{ft}$$

6. Step 6 — Check: returning L = 701.7 ft to

   $$Lat = L \cos(\theta)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 1,403 — kept a factor of two that cancels in the correct rearrangement.
• 350.9 — dropped that same factor in the other direction.
• 771.9 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Surveying → Latitudes and Departures

A surveying problem uses Traverse latitude. Given course length (L) = 426.0 ft; bearing angle (theta) = 74.0000 deg, determine the latitude (Lat) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Traverse latitude.
• Everything except Lat is given, so isolate Lat symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Surveying items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Lat = L \cos(\theta)$$

2. Step 2 — Rearrange the relation so that Lat stands alone on the left-hand side.

3. Step 3

   $$List the givens: course length (L) = 426.0 ft, bearing angle (theta) = 74.0000 deg$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$Lat = 117.4\ \text{ft}$$

6. Step 6 — Check: returning Lat = 117.4 ft to

   $$Lat = L \cos(\theta)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 234.8 — kept a factor of two that cancels in the correct rearrangement.
• 58.7108 — dropped that same factor in the other direction.
• 129.2 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Surveying → Latitudes and Departures

A surveying problem uses Traverse latitude. Given bearing angle (theta) = 6.0000 deg; latitude (Lat) = 294.1 ft, determine the course length (L) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Traverse latitude.
• Everything except L is given, so isolate L symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Surveying items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Lat = L \cos(\theta)$$

2. Step 2 — Rearrange the relation so that L stands alone on the left-hand side.

3. Step 3

   $$List the givens: bearing angle (theta) = 6.0000 deg, latitude (Lat) = 294.1 ft$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$L = 295.7\ \text{ft}$$

6. Step 6 — Check: returning L = 295.7 ft to

   $$Lat = L \cos(\theta)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 591.4 — kept a factor of two that cancels in the correct rearrangement.
• 147.9 — dropped that same factor in the other direction.
• 325.3 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Surveying → Latitudes and Departures

A surveying problem uses Traverse latitude. Given course length (L) = 60.0000 ft; bearing angle (theta) = 41.0000 deg, determine the latitude (Lat) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Traverse latitude.
• Everything except Lat is given, so isolate Lat symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Surveying items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Lat = L \cos(\theta)$$

2. Step 2 — Rearrange the relation so that Lat stands alone on the left-hand side.

3. Step 3

   $$List the givens: course length (L) = 60.0000 ft, bearing angle (theta) = 41.0000 deg$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$Lat = 45.2826\ \text{ft}$$

6. Step 6 — Check: returning Lat = 45.2826 ft to

   $$Lat = L \cos(\theta)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 90.5651 — kept a factor of two that cancels in the correct rearrangement.
• 22.6413 — dropped that same factor in the other direction.
• 49.8108 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Surveying → Latitudes and Departures

A surveying problem uses Traverse latitude. Given bearing angle (theta) = 54.0000 deg; latitude (Lat) = 542.1 ft, determine the course length (L) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Traverse latitude.
• Everything except L is given, so isolate L symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Surveying items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Lat = L \cos(\theta)$$

2. Step 2 — Rearrange the relation so that L stands alone on the left-hand side.

3. Step 3

   $$List the givens: bearing angle (theta) = 54.0000 deg, latitude (Lat) = 542.1 ft$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$L = 922.3\ \text{ft}$$

6. Step 6 — Check: returning L = 922.3 ft to

   $$Lat = L \cos(\theta)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 1,845 — kept a factor of two that cancels in the correct rearrangement.
• 461.1 — dropped that same factor in the other direction.
• 1,015 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Surveying → Latitudes and Departures

A surveying problem uses Traverse latitude. Given course length (L) = 138.0 ft; bearing angle (theta) = 73.0000 deg, determine the latitude (Lat) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Traverse latitude.
• Everything except Lat is given, so isolate Lat symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Surveying items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Lat = L \cos(\theta)$$

2. Step 2 — Rearrange the relation so that Lat stands alone on the left-hand side.

3. Step 3

   $$List the givens: course length (L) = 138.0 ft, bearing angle (theta) = 73.0000 deg$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$Lat = 40.3473\ \text{ft}$$

6. Step 6 — Check: returning Lat = 40.3473 ft to

   $$Lat = L \cos(\theta)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 80.6946 — kept a factor of two that cancels in the correct rearrangement.
• 20.1736 — dropped that same factor in the other direction.
• 44.3820 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Surveying → Latitudes and Departures

A surveying problem uses Traverse latitude. Given bearing angle (theta) = 65.0000 deg; latitude (Lat) = 279.1 ft, determine the course length (L) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Traverse latitude.
• Everything except L is given, so isolate L symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Surveying items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Lat = L \cos(\theta)$$

2. Step 2 — Rearrange the relation so that L stands alone on the left-hand side.

3. Step 3

   $$List the givens: bearing angle (theta) = 65.0000 deg, latitude (Lat) = 279.1 ft$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$L = 660.4\ \text{ft}$$

6. Step 6 — Check: returning L = 660.4 ft to

   $$Lat = L \cos(\theta)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 1,321 — kept a factor of two that cancels in the correct rearrangement.
• 330.2 — dropped that same factor in the other direction.
• 726.4 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Surveying → Latitudes and Departures

A surveying problem uses Traverse latitude. Given course length (L) = 262.0 ft; bearing angle (theta) = 22.0000 deg, determine the latitude (Lat) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Traverse latitude.
• Everything except Lat is given, so isolate Lat symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Surveying items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Lat = L \cos(\theta)$$

2. Step 2 — Rearrange the relation so that Lat stands alone on the left-hand side.

3. Step 3

   $$List the givens: course length (L) = 262.0 ft, bearing angle (theta) = 22.0000 deg$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$Lat = 242.9\ \text{ft}$$

6. Step 6 — Check: returning Lat = 242.9 ft to

   $$Lat = L \cos(\theta)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 485.8 — kept a factor of two that cancels in the correct rearrangement.
• 121.5 — dropped that same factor in the other direction.
• 267.2 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Surveying → Latitudes and Departures