Final answer:
To find the angle of depression from point A to point C, we can use the tangent function. By setting up a trigonometric equation using the given distance and angle, we can solve for the horizontal distance and find the angle of depression. None of the provided answer choices are correct.
Step-by-step explanation:
To find the angle of depression from point A to point C, we need to use the given information of distance and angle. The angle of depression is the angle formed between a horizontal line and the line of sight from an observer to a point below the observer. In this case, point A is above point C, so the angle of depression is the angle from the horizontal line to the line connecting points A and C.
To find the angle of depression, we can use trigonometry. We know that the tangent of an angle in a right triangle is equal to the length of the side opposite the angle divided by the length of the side adjacent to the angle. In this case, the side opposite the angle of depression is the vertical distance from point A to point C, and the side adjacent to the angle is the horizontal distance from point A to point C.
Let's use the tangent function to find the angle of depression:
tan(angle of depression) = opposite/adjacent
tan(angle of depression) = vertical distance/horizontal distance
tan(angle of depression) = 6 mi / horizontal distance
Now we can substitute the given values into the equation and solve for the angle of depression:
tan(58°) = 6 mi / horizontal distance
horizontal distance = 6 mi / tan(58°)
horizontal distance ≈ 3.901 mi
So, the angle of depression from point A to point C is approximately 3.901 mi. Therefore, none of the provided answer choices (a, b, c, d) are correct.