If A-B perpendicular to A

Question

and
|A-B|=B/2
What is an angle between A and B

Question is from vector chapter

Plse help

Answer 1

|A|^2 + |A-B|^2 = (-B)^2
A^2 + (B/2)^2 = B^2
4A^2 = 3B^2
If you draw the vectors, you see that
tanθ = |A-B|/|A| = B/2A = 1/√3