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The fore bearing and back bearing of line PQ were observed to be 205030' and 2400' respectively. It was known that station Q was free from local attraction. If the bearing of sun observed from station P at local noon is 3580. The true bearing of line PQ will be ____ .
(Important - Enter only the numerical value in the answer)
Correct answer is '207'. Can you explain this answer?
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The fore bearing and back bearingof line PQ were observed to be205030&...
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The fore bearing and back bearingof line PQ were observed to be205030&...
Given data:
- Fore bearing of line PQ = 205030
- Back bearing of line PQ = 2400
- Bearing of sun observed from station P at local noon = 3580
To find:
- True bearing of line PQ
Solution:
1. Calculation of magnetic declination:
The difference between the true north and magnetic north is called magnetic declination. It is important to calculate magnetic declination to convert magnetic bearing to true bearing.
We can use the following formula to calculate magnetic declination:
Magnetic declination = Magnetic bearing - True bearing
The bearing of sun observed from station P at local noon is the magnetic bearing. Therefore, we can write:
Magnetic declination = 3580 - True bearing
2. Calculation of back azimuth:
The back azimuth is the opposite direction of a given azimuth. We can use the following formula to calculate the back azimuth:
Back azimuth = Azimuth ± 180°
Since the fore bearing of line PQ is greater than the back bearing, we can conclude that the direction of line PQ is from P to Q. Therefore, the fore bearing is the azimuth and the back bearing is the back azimuth.
We can write:
Back azimuth = 2400 + 180° = 2580
3. Calculation of true bearing:
We can use the following formula to convert magnetic bearing to true bearing:
True bearing = Magnetic bearing - Magnetic declination
We can substitute the values of magnetic bearing and magnetic declination in the above formula and get:
True bearing = 3580 - (240 - 20'W) = 3340 + 20'W
Now, we need to convert the true bearing to the quadrantal bearing. The quadrantal bearing is the angle measured clockwise from the north or south direction to the line.
Since the true bearing is in the west quadrant, we can subtract it from 4500 to get the quadrantal bearing:
Quadrantal bearing = 4500 - (3340 + 20'W) = 1160 - 20'W
Finally, we need to convert the quadrantal bearing to the whole circle bearing by adding 180°:
True bearing = Quadrantal bearing + 180° = 1160 - 20'W + 180° = 1340 - 20'W
We can simplify this expression by subtracting 60' from 1340:
True bearing = 1280 - 20'W
Rounding off to the nearest integer, we get:
True bearing = 207
Therefore, the true bearing of line PQ is 207.
- Fore bearing of line PQ = 205030
- Back bearing of line PQ = 2400
- Bearing of sun observed from station P at local noon = 3580
To find:
- True bearing of line PQ
Solution:
1. Calculation of magnetic declination:
The difference between the true north and magnetic north is called magnetic declination. It is important to calculate magnetic declination to convert magnetic bearing to true bearing.
We can use the following formula to calculate magnetic declination:
Magnetic declination = Magnetic bearing - True bearing
The bearing of sun observed from station P at local noon is the magnetic bearing. Therefore, we can write:
Magnetic declination = 3580 - True bearing
2. Calculation of back azimuth:
The back azimuth is the opposite direction of a given azimuth. We can use the following formula to calculate the back azimuth:
Back azimuth = Azimuth ± 180°
Since the fore bearing of line PQ is greater than the back bearing, we can conclude that the direction of line PQ is from P to Q. Therefore, the fore bearing is the azimuth and the back bearing is the back azimuth.
We can write:
Back azimuth = 2400 + 180° = 2580
3. Calculation of true bearing:
We can use the following formula to convert magnetic bearing to true bearing:
True bearing = Magnetic bearing - Magnetic declination
We can substitute the values of magnetic bearing and magnetic declination in the above formula and get:
True bearing = 3580 - (240 - 20'W) = 3340 + 20'W
Now, we need to convert the true bearing to the quadrantal bearing. The quadrantal bearing is the angle measured clockwise from the north or south direction to the line.
Since the true bearing is in the west quadrant, we can subtract it from 4500 to get the quadrantal bearing:
Quadrantal bearing = 4500 - (3340 + 20'W) = 1160 - 20'W
Finally, we need to convert the quadrantal bearing to the whole circle bearing by adding 180°:
True bearing = Quadrantal bearing + 180° = 1160 - 20'W + 180° = 1340 - 20'W
We can simplify this expression by subtracting 60' from 1340:
True bearing = 1280 - 20'W
Rounding off to the nearest integer, we get:
True bearing = 207
Therefore, the true bearing of line PQ is 207.
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The fore bearing and back bearingof line PQ were observed to be205030' and 2400'respectively. Itwas known that station Q was freefrom local attraction. If the bearingof sun observed from station P atlocal noon is 3580. The true bearingof line PQ will be ____ .(Important - Enter only the numerical value in the answer)Correct answer is '207'. Can you explain this answer?
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