Directly below a 50m. high cliff is the side of a river. How wide is the river if the angle of depression from the edge of the cliff to the other side of the river is 57.68 degree

Tan =

Tan 57.68 = 50/D. D = ?.

To find the width of the river, we can use trigonometry and the given information of the angle of depression.

Let's assume that the width of the river is represented by "x" meters.

When we lower our line of sight from the top of the cliff to the other side of the river, we form a right-angled triangle. The vertical height of this triangle is 50 meters (height of the cliff), and the angle of depression is 57.68 degrees.

Using trigonometry, the tangent function is useful for finding the width of the river:

tan(angle) = opposite/adjacent

In this case, the angle is 57.68 degrees, the opposite side is the height of the cliff (50 meters), and the adjacent side is the width of the river (x meters). Therefore, we can write:

tan(57.68) = 50/x

Now, we can solve for x by rearranging the equation:

x = 50/tan(57.68)

Using a calculator, we can evaluate the tangent of 57.68 degrees and then divide 50 by that result to find the width of the river, x.

x ≈ 50 / tan(57.68) ≈ 59.82 meters

Thus, the width of the river is approximately 59.82 meters.