A student cycles 14km east from A and then 10km south east to B. Find the distance and bearing of B from A.

Answer 1

To find the distance between A and B, we can use Pythagoras' theorem.

The distance east from A to B is 14km, and the distance south east is 10km. So, we can consider this as a right-angled triangle. Let the distance between A and B be x km.

Therefore, x^2 = 14^2 + 10^2
x^2 = 196 + 100
x^2 = 296
x = √296
x = 17.2 km

So, the distance between A and B is 17.2 km.

To find the bearing of B from A, we need to find the angle that the line segment AB makes with the north direction. This can be found using trigonometry.

tan θ = opposite/adjacent
tan θ = 10/14
θ = tan^(-1)(10/14)
θ ≈ 35.5°

Therefore, B is located 17.2 km away from A at a bearing of approximately 35.5° south of east.