To determine how far off course the aircraft is after flying for 30 minutes at 550 knots and 2 degrees 30 minutes off course, we can use basic trigonometry.
First, we need to convert the time flown into hours since the speed is given in knots (nautical miles per hour).
Step 1: Convert time to hours
\[ 30 \text{ minutes} = \frac{30}{60} \text{ hours} = 0.5 \text{ hours} \]
Step 2: Calculate the distance traveled
\[ \text{Distance} = \text{Speed} \times \text{Time} \] \[ \text{Distance} = 550 \text{ knots} \times 0.5 \text{ hours} = 275 \text{ nautical miles} \]
Step 3: Convert the angle into radians
The angle given is 2 degrees 30 minutes, which we need to convert into decimal degrees. \[ 2 \text{ degrees} + \frac{30}{60} \text{ degrees} = 2.5 \text{ degrees} \]
To find the distance off course, we can use the sine function:
- Convert degrees to radians for calculations: \[ 2.5 \text{ degrees} = 2.5 \times \frac{\pi}{180} \text{ radians} \]
Step 4: Calculate the off-course distance using the sine function
The distance off course (d) can be found using: \[ d = \text{Distance} \times \sin(\text{angle in radians}) \]
So, we first calculate the sine of the angle in radians: \[ \text{angle in radians} = 2.5 \times \frac{\pi}{180} \approx 0.043633 \text{ radians} \] \[ \sin(0.043633) \approx 0.043619 \]
Now we find the distance off course: \[ d = 275 \text{ nautical miles} \times \sin(2.5^\circ) \approx 275 \times 0.043619 \approx 12.0 \text{ nautical miles} \]
Conclusion:
The aircraft is approximately 12 nautical miles off course.
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