A cliff on the bank of a river is 300 meter high. if the angle of depression of a point on the opposite side of the river is \(60^\circ\), find the width of...

The problem involves finding the width of a river given the height of a cliff and the angle of depression of a point on the opposite side of the river. The angle of depression is the angle formed between the horizontal line and the line of sight from the point on the opposite side of the river to the top of the cliff. We can use trigonometry to solve the problem. Let x be the width of the river. Then we have a right triangle with the height of the cliff as the opposite side, x as the adjacent side, and the angle of depression as 60 degrees. Using the tangent function, we have: tan(60) = opposite/adjacent sqrt(3) = 300/x x = 300/sqrt(3) x = 100sqrt(3) Therefore, the width of the river is 100sqrt(3) meters. So, the correct option is: - 100 - 75√3 m - 100√3m -  200√3m (100√3m) is the correct answer.