There is a plane arriving into Denver, CO. The plane is landing with an angle of depression of 42°. The plane is 18,000 feet off of the ground. Find how far the plane will travel horizontally before hitting the ground. (Round to the nearest hundredth)
no way to know without knowing the plane's speed.
To find how far the plane will travel horizontally before hitting the ground, we need to use trigonometry. The angle of depression (42°) is the angle formed between the horizontal ground and the line of sight downwards from the observer to the plane. The plane is 18,000 feet above the ground, which is the vertical distance.
Let's use the tangent function, which relates the opposite (vertical distance) to the adjacent (horizontal distance) side of a right triangle. In this case, the tangent of the angle of depression will give us the ratio between the vertical distance and the horizontal distance.
tan(42°) = opposite/adjacent
Let's replace the opposite side with 18,000 feet (the vertical distance):
tan(42°) = 18,000/adjacent
To find the adjacent side (horizontal distance), we rearrange the equation:
adjacent = 18,000/tan(42°)
Now, let's solve for the adjacent side using a calculator.
adjacent = 18,000 / tan(42°) ≈ 18,000 / 0.9004 ≈ 19,982.25
Therefore, the plane will travel approximately 19,982.25 feet horizontally before hitting the ground. Rounded to the nearest hundredth, this distance is 19,982.26 feet.