An aircraft starts to fly from A to B a distance of 140 kilometres, B being due north of A. The aircraft flies on a course 18 degrees east of north for a distance of 80 kilometres. Calculate how far the aircraft is then from the line AB and in what direction it should then fly to reach B

To calculate how far the aircraft is from the line AB, we need to find the perpendicular distance from the point where the aircraft changes course to the line AB.

The aircraft has flown 80 km on a course 18 degrees east of north. This means it has flown 80*cos(18) km north and 80*sin(18) km east.

The aircraft is now 80*sin(18) km east of point A.

To find the perpendicular distance from this point to the line AB, we can draw a right triangle with one leg being the distance from A to the point where the aircraft changes course (80*cos(18) km) and the other leg being the distance from the point where the aircraft changes course to the line AB (80*sin(18) km).

Using the Pythagorean theorem, we can calculate the perpendicular distance as follows:

Perpendicular distance = sqrt((80*sin(18))^2 - (80*cos(18))^2)
Perpendicular distance = sqrt((80*sin(18))^2 - (80*cos(18))^2)
Perpendicular distance = sqrt((80*sin(18))^2 - (80*cos(18))^2)
Perpendicular distance = sqrt(1577.284) km
Perpendicular distance ≈ 39.72 km

So, the aircraft is approximately 39.72 km from the line AB.

To reach point B, the aircraft needs to fly due north for the remaining distance. This means the aircraft should fly directly north for 140 km - 80 km = 60 km.