A Plane flies 400km west then 100km north find it's distance and bearing from it starting point with a suitable digram

Answer 1

To find the distance and bearing of the plane from its starting point, we can use the Pythagorean theorem and trigonometry.

First, let's draw a diagram:

```
P A
*--------->
| |
| |
| |
| |
v ^
B C
```

In this diagram, the starting point of the plane is point A, and it has flown 400km west to point B and then 100km north to point C. Point P represents the position we want to find: the distance and bearing of the plane from A.

To find the distance PA, we can use the Pythagorean theorem:

```
PA^2 = PB^2 + AB^2
PA^2 = 400^2 + 100^2
PA^2 = 160000 + 10000
PA^2 = 170000
PA = √170000
PA ≈ 412.3 km
```

So the plane is about 412.3km from its starting point.

To find the bearing of the plane from its starting point, we can use trigonometry. We want to find angle x, which is the angle between the line AB (which points due west) and the line PA.

```
tan(x) = BC/AB
tan(x) = 100/400
tan(x) = 0.25
x ≈ 14.0 degrees
```

So the bearing of the plane from its starting point is 14.0 degrees (measured clockwise from due east).

Therefore, we can conclude that the plane is about 412.3km away from its starting point, and is bearing 14.0 degrees (measured clockwise from due east) from that point.