Question

The pit bottom in a correlation survey is shown in the figure. Points C and D represent two suspended wires. The bearing of line CD is 286°00'00'' and its length is 4.64 m. The angle CED is measured as 00°00'40''. The length of line DE is 5.46 m. Considering the Weisbach triangle method, the bearing of the line CE is 

• A. 286°00'47''
• B. 285°59'12.9''
• C. 286°00'40''
• D. 285°00'47.1''

Hint:

In the Weisbach method, the law of sines is used to relate angles and sides of the triangle formed by the points.

Answer 1

The Correct Option is B

We are given the following data:
- Bearing of line CD = 286°00'00''
- Angle CED = 00°00'40''
- Length of CD = 4.64 m
- Length of DE = 5.46 m

Step 1: Applying the Weisbach triangle method.
The Weisbach triangle method involves using a triangle formed by three points, where we know two sides and the included angle. We use the law of sines to calculate the bearing of the third side, which is line CE. The formula to calculate the bearing of line CE is: \[ \sin(\text{bearing of CE}) = \frac{\sin(\text{angle CED})}{\text{length of CD}} \times \text{length of DE} \]
Substituting the known values: \[ \sin(\text{bearing of CE}) = \frac{\sin(00°00'40'')}{4.64} \times 5.46 \]
After solving this equation, we find that the bearing of line CE is approximately: \[ \boxed{285°59'12.9''}. \]

Final Answer: 285°59'12.9''