Final answer:
The distance of the plane from Dubbo is approximately 778 km.
Step-by-step explanation:
To find the distance from Dubbo to the plane, we need to calculate the distance the plane traveled along its flight path. The plane first flies on a bearing of 139° for 852 km, and then turns and flies on a bearing of 285° until it is due west of Dubbo. We can break down the plane's displacement into its north-south and east-west components.
Using vector addition, we can find the north-south and east-west distances.
North-south component: Distance = 852 km × sin(139° - 180°) = -454.19 km (negative because it's going south)
East-west component: Distance = 852 km × cos(139° - 180°) = -625.88 km (negative because it's going west)
To find the distance from Dubbo, we use the Pythagorean theorem: Distance = √((-454.19 km)^2 + (-625.88 km)^2) = 778 km (rounded to the nearest km).