you first walk 8.0km north from home then walk east until your displacement from home is 10.0 km. How far east did you walk?

Answer 1

Assuming you are not near the poles, you can calculate the distances by the Pythagoras theorem.

North and east are perpendicular to each other, and the hypothenuse sought is 10 km, with one leg being 8 km. What is the length of the other leg, x, if according to Pythagoras,
10^sup2; = 8² + x²