Calculate the lenght of the return journey from point c to point a when an aircraft flies from its base a 200km on a bearing of 162 degrees to point b,then flies 350km on a bearing of 160 degrees to point c,and then return directly to base a
planes fly on headings, not bearings.
Man, those two headings are almost the same. The distance will be very nearly 200+350.
However, using the law of cosines, the distance z is
z^2 = 200^2 + 350^2 - 2*200*350*cos178°
To calculate the length of the return journey from point C to point A, we need to break down the problem into smaller steps and use trigonometry.
Step 1: Find the coordinates of each point.
Let's assume the base point A is (0, 0). Point B is located 200 km away at a bearing of 162 degrees, and point C is located 350 km away at a bearing of 160 degrees. To calculate the coordinates of point B and point C, we can use the formulas:
x = distance * sin(bearing)
y = distance * cos(bearing)
For point B:
x = 200 km * sin(162 degrees)
y = 200 km * cos(162 degrees)
For point C:
x = 350 km * sin(160 degrees)
y = 350 km * cos(160 degrees)
Step 2: Calculate the distance from point C to point A.
The distance between two points can be calculated using the formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, we want to find the distance between point C and point A:
distance_CA = sqrt((xC - 0)^2 + (yC - 0)^2)
Step 3: Calculate the distance of the return journey.
Since the aircraft returns directly from point C to point A, the distance of the return journey is the same as the distance from point C to point A.
Let's put the numbers into the formulas and calculate the values:
For point B:
x_B = 200 km * sin(162 degrees)
y_B = 200 km * cos(162 degrees)
For point C:
x_C = 350 km * sin(160 degrees)
y_C = 350 km * cos(160 degrees)
Distance_CA = sqrt((x_C - 0)^2 + (y_C - 0)^2)
Finally, the length of the return journey from point C to point A is: Distance_CA.