A plane is 160 miles north and 85 miles east of an airport. If the pilot wants to fly directly to the airport, what bearing would be taken?

To find the bearing, we can use trigonometry.

First, let's draw a diagram:

```
* Plane
|
| N
| |
| |
|---|---| Airport
| |
85 160
```

We can use the formula `tan(bearing) = opposite / adjacent` to find the bearing.

In this case, the opposite side is 160 miles (north), and the adjacent side is 85 miles (east).

So, `tan(bearing) = 160 / 85`

To find the actual bearing, we need to take the inverse tangent (arctan) of this ratio.

Using a calculator to find the inverse tangent of `160 / 85`, we get:

`bearing = arctan(160 / 85)`

The approximate value of `bearing` is 62.1 degrees.

Therefore, the pilot should take a bearing of approximately 62.1 degrees to fly directly to the airport.

To find the bearing, we need to determine the angle (in degrees) between the plane's position and the north direction. Here's how you can do this:

Step 1: Draw a diagram:
Start by drawing a coordinate plane and mark the airport as the origin (0, 0). Then, plot the plane's position 160 miles north and 85 miles east of the airport.

Step 2: Create a right triangle:
Connect the plane's position with the airport to form a right triangle. The vertical side of the triangle represents the north direction, and the horizontal side represents the east direction.

Step 3: Find the length of the hypotenuse:
Use the Pythagorean theorem to find the length of the hypotenuse (the line connecting the plane and the airport). The hypotenuse is the shortest distance between two points, which represents the direct path the plane should take to reach the airport.

Applying the Pythagorean theorem:
The length of the hypotenuse can be found using the formula: c^2 = a^2 + b^2, where c is the hypotenuse, and a and b are the lengths of the other two sides.

In this case, a = 160 miles (north) and b = 85 miles (east). Thus,
c^2 = (160)^2 + (85)^2
c^2 = 25600 + 7225
c^2 = 32825
c ≈ 181.14 miles (approx.)

Step 4: Calculate the bearing:
To find the bearing, we need to determine the angle between the hypotenuse (the line connecting the plane and the airport) and the north direction.

Use trigonometry to find this angle:
tan(θ) = opposite/adjacent
tan(θ) = 85/160
θ ≈ 27.0° (approx.)

The bearing is measured clockwise from north, so the plane would take a bearing of approximately 27 degrees.

make a sketch, you know the bearing will be something like

S Ø W
and the angle Ø will be the same as the angle inside your right_angled triangle so that
tanØ = 85/160 = .53125
Ø = 27.979..° or appr 28°

So , S 28° W