The depth of the gorge is approximately 92.33 meters.
The angle of depression refers to the angle formed between a horizontal line and the line of sight when an observer looks downward from a higher point to see an object or a point that is lower than the observer's position.
In this case, the angle of depression of the bottom corner of the gorge is 72 degrees when viewed from the opposite edge. So, if someone stands at the edge of the gorge and looks down towards the bottom corner, they would need to look at a downward angle of 72 degrees from the horizontal line to see that corner.
To calculate the depth of the gorge, you can use trigonometry. Given that the gorge has a width of 60 meters and the angle of depression is 72 degrees, you can use the tangent function:
tan(angle of depression) = opposite side / adjacent side
Here, the opposite side is the depth of the gorge, and the adjacent side is half of the width (since the observer is looking from the midpoint of the width to the bottom corner).
Let's denote the depth of the gorge as "d":
tan(72 degrees) = d / (60 m / 2)
tan(72 degrees) = d / 30
d = 30 * tan(72 degrees)
Using a calculator:
d ≈ 30 * 3.07768
d ≈ 92.33 meters
Therefore, the depth of the gorge is approximately 92.33 meters.