To find the distance the plane still needs to fly to reach the ground, we can use the concept of right triangles. The altitude of the plane (1,000 feet) will be one leg of the right triangle, and the distance the plane still needs to fly (let's call it \(d\)) will be the hypotenuse. The angle of depression (12°) is the angle between the horizontal line and the line of descent.
In this scenario, we can use the sine function, which relates the opposite side (the altitude) to the hypotenuse (the distance to the ground):
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
Here, \(\theta\) is 12°, the opposite side is the altitude (1,000 feet), and the hypotenuse is \(d\):
\[ \sin(12°) = \frac{1000}{d} \]
We can rearrange this equation to solve for \(d\):
\[ d = \frac{1000}{\sin(12°)} \]
Next, we calculate \(\sin(12°)\):
\[ \sin(12°) \approx 0.2079 \]
Now we can substitute this value back into our equation for \(d\):
\[ d = \frac{1000}{0.2079} \approx 4811.57 \]
Rounding \(d\) to the nearest foot, we get:
\[ d \approx 4812 \text{ feet} \]
So, the distance the plane still needs to fly to reach the ground is approximately 4,812 feet.
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