Answer:
,
(Northeast)
Step-by-step explanation:
Let consider that owner has the resultant direction of the momentums from the dog and the cat. First, the momentum of the owner is:
![\|\vec p \| = \sqrt{\left[(27.4\,kg)\cdot \left(2.19\,(m)/(s) \right)\right]^(2)+\left[(7.19\,kg)\cdot \left(2.78\,(m)/(s) \right)\right]^(2)}](https://img.qammunity.org/2021/formulas/physics/college/3lga5pi4d47vyc5r6re1aqlt3mpe5qwrus.png)

The speed of the owner is:


Lastly, the direction of the owner is:
![\alpha = \tan^(-1)\left[((27.4\,kg)\cdot \left(2.19\,(m)/(s) \right))/((7.19\,kg)\cdot \left(2.78\,(m)/(s) \right)) \right]](https://img.qammunity.org/2021/formulas/physics/college/qu3a1bvyu99ib1rr4iy0xhsm2blrey5qs8.png)
(Northeast)