If a plane flies at 56 km/h at a bearing of 65 degrees for 3 hours and then changes to a bearing of 90 degrees for another hour at the same speed, what is the plane's bearing from its original position?

To determine the plane's bearing from its original position, we need to break down its journey into two segments based on the information provided.

In the first part of the journey, the plane flies at a speed of 56 km/h for 3 hours at a bearing of 65 degrees. We can calculate the distance covered in this segment by multiplying speed by time, which gives us 56 km/h * 3 h = 168 km.

For this leg of the flight, we can determine the northward and eastward components of this distance using trigonometry. The northward component can be calculated using the cosine of the bearing angle, while the eastward component uses the sine of the angle:

• Northward distance = 168 km * cos(65 degrees)

• Eastward distance = 168 km * sin(65 degrees)

Next, for the second part of the journey, the plane flies at the same speed and for a duration of 1 hour at a bearing of 90 degrees. In this case, the distance covered is simply 56 km (since the plane flies for 1 hour). At a bearing of 90 degrees, this distance moves directly eastwards with no northward component:

• Northward distance =