Let's denote the width of the river as x.

The angle of depression is the angle formed by a horizontal line and the line of sight to an object below the horizontal line.

In this case, we can draw a right triangle with the horizontal leg representing the width of the river, the vertical leg representing the height of the cliff, and the hypotenuse representing the line of sight from the top of the cliff to the point on the opposite side of the river.

The angle of depression is 60º, so the angle between the horizontal leg and the hypotenuse is also 60º.

Since this is a right triangle, we can use trigonometry to find x. The tangent of an angle in a right triangle is equal to the ratio of the length of the side opposite to the angle to the length of the side adjacent to the angle. So, we have:

\(\tan(60^\circ) = \frac{300}{x}\)

\(x = \frac{300}{\tan(60^\circ)}\)

The exact value of \(\tan(60^\circ)\) is \(\sqrt{3}\), so we get:

\(x = \frac{300}{\sqrt{3}}\)

\(= \frac{300\sqrt{3}}{\sqrt{3}\sqrt{3}}\)

\(= \frac{300\sqrt{3}}{3}\)

\(= 100\sqrt{3}\)

So, the width of the river is 100\(\sqrt{3}\) meters.