An airplane trip involves three legs, with two stopovers, the first leg is due northeast 375 miles at 30° (from Y-Axis), the second leg is southeast for 440 Km at 50° (from Y- Axis), and the third leg is at 37º south of west for 550 Km what is the plane total displacement in miles and direction in degrees?

To solve this problem, we need to break down each leg of the trip into its x and y components, add them up, and then use the Pythagorean theorem to find the total displacement. We also need to convert all distances to the same units, so let's convert kilometers to miles (1 km = 0.621371 miles).

1. First leg: 375 miles at 30° from the Y-axis X1 = 375 cos(30) = 324.92 miles Y1 = 375 sin(30) = 187.5 miles

2. Second leg: 440 km at 50° from the Y-axis Convert 440 km to miles: 440 * 0.621371 = 273.4 miles X2 = 273.4 cos(50) = 175.77 miles Y2 = 273.4 sin(50) = 209.68 miles

3. Third leg: 550 km at 37° south of west Convert 550 km to miles: 550 * 0.621371 = 341.75 miles Since it's south of west, we consider the x component as negative and the y component as positive. X3 = -341.75 cos(37) = -273.27 miles Y3 = 341.75 sin(37) = 204.68 miles

Now, add up the x and y components: X_total = X1 + X2 + X3 = 324.92 + 175.77 - 273.27 = 227.42 miles Y_total = Y1 + Y2 + Y3 = 187.5 + 209.68 + 204.68 = 601.86 miles

The total displacement can be found using the Pythagorean theorem: Displacement = sqrt(X_total^2 + Y_total^2) = sqrt((227.42)^2 + (601.86)^2) = 648.5 miles

The direction can be found using the arctan function: Direction = arctan(Y_total / X_total) = arctan(601.86 / 227.42) = 69.4° from the Y-axis.

So, the total displacement of the plane is approximately 648.5 miles in the direction 69.4° from the Y-axis.