A surveyor stands on one edge of a ravine. She determines that the ravine w is 140 feet wide. She then determines that the angle of depression from the edge where she is standing to a point on the bottom of the ravine a is 57.5°, as shown in figure below (which is not to scale). How deep is the ravine?
123
To find the depth of the ravine, we can use trigonometry, specifically the tangent function.
Let's assume that the depth of the ravine is represented by the variable "d".
In the given problem, we know the width of the ravine (w) is 140 feet, and we have the angle of depression (θ) of 57.5°.
Now, consider a right triangle formed by the surveyor's position, the point on the bottom of the ravine, and a point directly beneath the surveyor on the same vertica