A plane flies 510 kilometers with a bearing of N43 degrees W from airport B to airport C. The plane then flies SW 790 kilometers from C to A which is due west of B. Find bearing of flight from C to A.
planes fly on headings
distant objects have bearings
I thought you said the plane flew SW from C to A. Why then do you ask for it?
Typo?
50°and
To find the bearing of the flight from airport C to airport A, we can use trigonometry and the information given.
First, let's visualize the situation:
Airport B is the starting point, and we are given that the plane flies 510 kilometers with a bearing of N43°W from B to C. This means that the angle made by the flight path and the direction due west is 43°. So, we can represent the flight path from B to C as follows:
N43°W
|
|
|------> 510 km
Now, the plane flies 790 kilometers from airport C to airport A in a southwest direction.
To find the bearing of the flight from C to A, we need to determine the angle between the flight path from C to A and the direction due west.
First, we need to find the angle between the flight path from C to A and the x-axis (the direction due west). We can do this by using the inverse tangent function:
tan(θ) = Opposite / Adjacent
Since we have the length of the adjacent side (790 km) and the length of the opposite side (510 km), we can find the value of θ:
θ = atan(510 km / 790 km)
≈ 32.6°
The angle θ represents the angle between the flight path from C to A and the x-axis.
Next, we need to find the angle between the flight path from C to A and the y-axis (north direction). To do this, we subtract the angle between the flight path from B to C (43°) from the angle θ:
Angle between flight path from C to A and y-axis = θ - 43°
= 32.6° - 43°
≈ -10.4°
Note: In this context, a negative angle (-10.4°) indicates a southward deviation from the y-axis.
Finally, to determine the bearing of the flight from C to A, we need to express the angle in compass notation:
Bearing of the flight from C to A:
Angle from the north direction = 180° - (Angle between flight path from C to A and y-axis)
= 180° - (-10.4°)
= 190.4°
Therefore, the bearing of the flight from airport C to airport A is approximately N10.4°W.