Distance Departure Difference of Latitude
544 272.0 471.1
546 273.0 472.8
Find the departure (Dep) at a distance of 545.3 Nm. Write your answer to the nearest hundredth.
Using linear interpolation, we can find the departure at a distance of 545.3 Nm.
First, we need to determine the difference in latitude between the given distances 544 Nm and 546 Nm.
Difference in Latitude = 472.8 - 471.1 = 1.7
Next, we can calculate the departure at a distance of 545.3 Nm using the formula:
Departure = Departure at 544 Nm + ((545.3 - 544) / (546 - 544)) * Difference in Latitude
Departure = 272.0 + ((545.3 - 544) / (546 - 544)) * 1.7
Departure ≈ 272.85
Therefore, the departure at a distance of 545.3 Nm is approximately 272.85 Nm (to the nearest hundredth).
To find the departure at a distance of 545.3 Nm, we can use the concept of interpolation.
Interpolation is the estimation of a value within two known values in a sequence of values. In this case, we need to interpolate the departure value between the given distances of 544 Nm and 546 Nm.
First, let's calculate the difference in latitude between the two given distances:
Difference in Latitude = 472.8 - 471.1 = 1.7
Next, we need to calculate the rate of change of departure per unit distance (slope):
Rate of Change of Departure = (273.0 - 272.0) / (546 - 544) = 1 / 2 = 0.5
Now, we can use the following formula to find the departure at a distance of 545.3 Nm:
Dep = Departure at lower distance + (Difference in Latitude) × (Rate of Change of Departure)
Dep = 272.0 + (545.3 - 544) × 0.5 = 272 + 1.3 × 0.5 = 272 + 0.65 = 272.65
Therefore, the departure at a distance of 545.3 Nm is approximately 272.65 Nm.