1. A closed traverse has the following data:

COURSE

BEARING

DISTANCE

A-B

N 9.27° E

58.7 m

B-C

S 88.43° E

27.3 m

C-D

N 86.73° E

35.2 m

D-E

S5.3° E

35.0 m

E-A

Table 10

Compute the bearing and the distance of line E-A.

To solve for the **bearing** and **distance** of line E-A in a closed traverse, we need to first understand the approach using a mathematical method called **traverse computation**. Here's the outline of the steps:

1. **Convert bearings to azimuths** for each course.
2. **Resolve each distance into its North-South and East-West components** using trigonometry (sine and cosine functions).
3. **Sum up the North-South and East-West components** for all courses.
4. **Calculate the total misclosure** in both North-South and East-West directions.
5. **Compute the distance and bearing of line E-A** using the misclosure values.

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### Step 1: Convert Bearings to Azimuths

Azimuths are measured from the North in a clockwise direction:
- **A-B**: \( \text{Bearing} = N 9.27^\circ E \Rightarrow \text{Azimuth} = 9.27^\circ \)
- **B-C**: \( \text{Bearing} = S 88.43^\circ E \Rightarrow \text{Azimuth} = 180^\circ - 88.43^\circ = 91.57^\circ \)
- **C-D**: \( \text{Bearing} = N 86.73^\circ E \Rightarrow \text{Azimuth} = 86.73^\circ \)
- **D-E**: \( \text{Bearing} = S 5.3^\circ E \Rightarrow \text{Azimuth} = 180^\circ + 5.3^\circ = 185.3^\circ \)

### Step 2: Resolve Each Distance into North-South and East-West Components

We now resolve each course's distance into its **Northing (N-S)** and **Easting (E-W)** components using sine and cosine:

- **A-B**: 
  - Northing: \( 58.7 \times \cos(9.27^\circ) \)
  - Easting: \( 58.7 \times \sin(9.27^\circ) \)

- **B-C**:
  - Northing: \( 27.3 \times \cos(91.57^\circ) \)
  - Easting: \( 27.3 \times \sin(91.57^\circ) \)

- **C-D**:
  - Northing: \( 35.2 \times \cos(86.73^\circ) \)
  - Easting: \( 35.2 \times \sin(86.73^\circ) \)

- **D-E**:
  - Northing: \( 35.0 \times \cos(185.3^\circ) \)
  - Easting: \( 35.0 \times \sin(185.3^\circ) \)

Let's compute these values.

### Step 3: Sum Northing and Easting Components

We add up all the Northings and Eastings to determine the total net change in North and East directions.

### Step 4: Calculate Misclosure and Compute Line E-A

The misclosure gives us the net discrepancy in the North-South and East-West directions, and from this, we can find the bearing and distance of line E-A.

Let me calculate these values step-by-step.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you need further clarification or help with any specific part of the solution, feel free to ask!

Here are five questions to expand your understanding:
1. How are azimuths related to bearings in traverse computations?
2. What is the purpose of resolving distances into Northing and Easting components?
3. How can we handle misclosure errors in a closed traverse?
4. What role does trigonometry play in surveying and traverse computations?
5. How do you compute the distance and bearing from coordinate differences?

**Tip:** Always double-check the quadrant for bearings when converting from azimuths to avoid mistakes.

A closed traverse has the following 

COURSE
BEARING
DISTANCE
A-B
N 9.27° E
58.7 m
B-C
S 88.43° E
27.3 m
C-D
N 86.73° E
35.2 m
D-E
S 5.3° E
35.0 m
E-A
Table 10
Compute the bearing and the distance of line E-A.

This problem involves calculating the bearing and distance of line E-A in a closed traverse, using azimuth conversion and trigonometry. Learn to apply formulas for resolving distances into Northing and Easting components to compute the bearing and distance. Suitable for undergraduate engineering students or advanced high school learners.

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