A good answer might be:

60.051°


Answer Worked Out

In loving detail:

  1. The endpoints are:
    (0, 3, 0) to (2, 0, 0)
    (0, 3, 0) to (0, 0, 4)
  2. The displacement vectors are:
    a  =  (2, 0, 0) - (0, 3, 0)  =  (2, -3, 0)T
    b  =  (0, 0, 4) - (0, 3, 0)  =  (0, -3, 4)T
  3. The lengths are:
    |a|2  =   (2, -3, 0)T ·  (2, -3, 0)T  =  13
    |b|2  =   (0, -3, 4)T ·  (0, -3, 4)T  =  25
  4. The normalized vectors are:
    au  =  (2, -3, 0)T / 13
    bu  =  (0, -3, 4)T / 5
  5. The dot product is:
    au · bu  =  (2, -3, 0)T · (0, -3, 4)T / (513)
    =  9 / (513)  =   0.49923
  6. The angle is:
    cos θ   =  0.49923
    θ  =  arc cos 0.49923  =  60.051°


QUESTION 12:

If you had calculated the displacement vectors in the opposite manner (by subtracting from (0, 3, 0) ) would it have affected the answer?