Set up the velocities

• Speed of swimmer in still water: $v_s = 12\ \text{km/h}$
• Speed of river flow: $v_r = 6\ \text{km/h}$

We want the swimmer to reach the point directly opposite, so the net velocity across the river must have no component along the river flow.

Choose direction carefully

Let the river flow be along the positive $x$-direction.

Suppose the swimmer swims at an angle $\theta$ with respect to the direction of flow.

Then the component of swimmer's velocity along the flow is: $12\cos\theta$

Since river itself flows with velocity $6\ \text{km/h}$ along the same direction, for no drifting, $12\cos\theta + 6 = 0$

Solve for the angle

$12\cos\theta = -6$ $\cos\theta = -\frac{1}{2}$

Therefore, $\theta = 120^\circ$

(The other cosine solution $240^\circ$ is not physically relevant here.)

Final answer

The swimmer should swim at an angle $\boxed{120^\circ}$ with respect to the direction of river flow.

Comparison with stored answer

Stored correct answer: $120$

Our derived answer matches the stored answer.