Distance Departure Difference of Latitude
544 272.0 471.1
546 273.0 472.8
Find the difference of latitude (Dlat) at a distance of 545.3 Nm. Write your answer to the nearest hundredth.
To find the difference of latitude (Dlat) at a distance of 545.3 Nm, we first need to find the relationship between distance and difference of latitude using the given data.
Using the given data:
Distance1 = 544 Nm
Departure1 = 272.0
Difference of Latitude1 = 471.1
Distance2 = 546 Nm
Departure2 = 273.0
Difference of Latitude2 = 472.8
We can calculate the slope (rate of change) between Distance and Difference of Latitude:
Slope = (Difference of Latitude2 - Difference of Latitude1) / (Distance2 - Distance1)
= (472.8 - 471.1) / (546 - 544)
= 1.7 / 2
= 0.85
Now, we can use this slope to find the difference of latitude at a distance of 545.3 Nm:
Distance = 545.3 Nm
Difference of Latitude = Difference of Latitude1 + (Distance - Distance1) * Slope
= 471.1 + (545.3 - 544) * 0.85
= 471.1 + 1.3 * 0.85
= 471.1 + 1.105
= 472.21
Therefore, the difference of latitude (Dlat) at a distance of 545.3 Nm is approximately 472.21 (rounded to the nearest hundredth).
To find the difference of latitude (Dlat) at a distance of 545.3 Nm, we can use interpolation.
1. First, calculate the departure difference per distance (DDPD) for the given data points:
DDPD = (Departure2 - Departure1) / (Distance2 - Distance1)
DDPD = (273.0 - 272.0) / (546 - 544)
DDPD = 1.0 / 2
DDPD = 0.5
2. Next, calculate the latitude difference (Dlat) at the given distance using the equation:
Dlat = Difference of Latitude1 + DDPD * (Given Distance - Distance1)
Dlat = 471.1 + 0.5 * (545.3 - 544)
Dlat = 471.1 + 0.5 * 1.3
Dlat = 471.1 + 0.65
Dlat = 471.75
So, the difference of latitude (Dlat) at a distance of 545.3 Nm is approximately 471.75.