A ship leaves point A and travels directly north to point B. From point B, the ship then travels due east to point C..

Question

The magnitude of the vector from point A to point C is 138. Find the magnitude of the northern vector. Find the magnitude of the eastern vector.

Answer 1

From the diagram, the line BD bisect the angle B and also bisect the line AC.

From the triangle BCD,

sin(45^o) =  CD/BC

1/√2 = 69/BC

BC = 69√2.

From the triangle BAD,

sin(45^o) =  AD/AB

1/√2 = 69/AB

AB = 69√2.

The magnitude of the northern vector = || AB || = 69√2.

The magnitude of the eastern vector = || BC || = 69√2.