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? (Round your answer to one decimal place.)

Question

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? (Round your answer to one decimal place.)

Answer 1

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Answer 2

To find the depth of the ravine, we can use trigonometry and the angle of depression provided.

Let's label the depth of the ravine as "d" (in feet).

From the given information, we have the opposite side (d) and the adjacent side (w/2) of the right triangle formed. The angle of depression is the angle between the hypotenuse (line of sight) and the horizontal line (ground).

Using the tangent function (tan), we can set up the following equation:

tan(angle) = opposite / adjacent

tan(57.5°) = d / (w/2)

To solve for "d," we rearrange the equation:

d = tan(57.5°) * (w/2)

Plugging in the given values:

d = tan(57.5°) * (140/2)

d ≈ 0.8004 * 70

d ≈ 56.03

Therefore, the depth of the ravine is approximately 56.0 feet.