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 on it should then fly to reach B?

Answer 1

To find how far the aircraft is from the line AB, we can consider the right triangle formed by the line AB, the direction the aircraft flew (18 degrees east of north), and the perpendicular distance from the aircraft to the line AB.

We can calculate the perpendicular distance using trigonometry. Let x be the perpendicular distance we need to find.

We know that the aircraft flew a distance of 80 km at an angle of 18 degrees east of north. This means the component of the distance that is perpendicular to the line AB is 80*sin(18).

Therefore, x = 80*sin(18) ≈ 25.65 km

So, the aircraft is approximately 25.65 km away from the line AB.

To find the direction the aircraft should fly on to reach B, we can consider the right triangle formed by the distance the aircraft still needs to cover to reach B and the perpendicular distance x we found.

Let θ be the angle between the line AB and the direction the aircraft should now fly.

We know that tan(θ) = x / (140-80*cos(18))

Plugging in the values we found:

tan(θ) = 25.65 / (140 - 80*cos(18))
θ ≈ 12.15 degrees

Therefore, the aircraft should fly at an angle of 12.15 degrees east of north to reach point B.