A helicopter flies 40km east followed by 105km south. On what bearing must the helicopter fly to return home directly?

To find the bearing the helicopter must fly to return home directly, we can use trigonometry.

First, let's draw a diagram to visualize the situation.

```
|
|
|
-------H-------
|
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|
```

In this diagram, H represents the starting point of the helicopter, and the lines represent the distances it flies in each direction.

We can see that the helicopter forms a right-angled triangle with sides of 40 km and 105 km.

To find the bearing, we need to find the angle between the east direction and the line connecting the starting point to the destination point.

Using trigonometry, we can find this angle by taking the inverse tangent of the ratio of the opposite side (105 km) to the adjacent side (40 km).

tan(angle) = opposite/adjacent
tan(angle) = 105/40
angle = arctan(105/40)

Using a calculator, we find that the angle is approximately 68.2 degrees.

Since the helicopter is flying south, the bearing is measured clockwise from the north direction.

Therefore, the bearing the helicopter must fly to return home directly is 360 degrees - 68.2 degrees = 291.8 degrees.

So, the helicopter must fly on a bearing of approximately 291.8 degrees to return home directly.