Question

An aeroplane flies 20km in a direction 60 degrees north of east, 30km straight east, then 10km straight north. How far and in what direction is the plane from the starting point?​

Answer 1

Explanation:

Let the aeroplane start at O. It flies 20 km in a direction 60 degrees north of east to A. A is thus 20*cos(60), namely 10 km east of O and 20*sin(60), namely 17.3 km north of O. From A, it flies 30 km to further east to a point B. B is thus (10+30), namely 40 km east of O and 17.3 km north of O. From B, it flies 10 km north to C. C is therefore 40 km east of O and (17.3+10), namely 27.3 km north of O. The distance OC is equal to sqrt(40^2 + 27.3^2), which is 48.4 km. C is arctan(27.3/40), namely 34.3 degrees north of east compared to the starting location O.