John intended to work on the bearing of 240 degree. His compass was not work properly so he actually worked 200m on the bearing of 225 degree what distance and what bearing should he walked to reach the place he intended to reach? Show with diagrams with bearing the journey of John.
First, we can calculate how far off John was from his intended destination:
Using trigonometry, we can calculate the horizontal and vertical components of the distance John walked.
Horizontal distance = 200m * cos(225°) = 200m * (-√2/2) ≈ -141.4m
Vertical distance = 200m * sin(225°) = 200m * (-√2/2) ≈ -141.4m
So, John walked approximately 141.4m to the southwest of his intended destination.
To find the actual distance and bearing John should walk to reach his intended destination, we can calculate a triangle with sides of 200m and 141.4m.
Using the Pythagorean theorem:
c² = a² + b²
c² = (200m)² + (141.4m)²
c² = 40000m² + 20000m²
c² = 60000m²
c ≈ √60000 ≈ 244.9m
So, John should walk approximately 244.9m in order to reach his intended destination.
Now, we can calculate the bearing John should walk. To calculate the angle with respect to the north, we can use the arctan function:
Angle = arctan(vertical distance / horizontal distance)
Angle = arctan(-141.4m / -141.4m) ≈ arctan(1) ≈ 45°
Since John started at 240 degrees and turned 45 degrees clockwise to reach his intended destination, the final bearing should be:
240° + 45° = 285°
Therefore, John should walk approximately 244.9m on a bearing of 285 degrees to reach his intended destination.
Below is a diagram showing John's journey:
```
| /
| /
| /
|/
O-------------X
```
Where O is John's starting point, X is his intended destination, and the line shows the path he actually walked.
John's intended destination is on a bearing of 240° and he should walk on a bearing of 285° to reach it.