To find the distance the plane still needs to fly to reach the ground, we can use some trigonometry.
Given:
- The angle of depression is 12 degrees.
- The current altitude of the plane is 1,000 feet.
The distance the plane still needs to fly (which we will denote as \(d\)), the altitude (which we denote as \(h\)), and the angle of depression create a right triangle where:
- \(h\) (the altitude) is the opposite side,
- \(d\) (the distance to the ground) is the hypotenuse, and
- the angle of depression is given.
We can use the sine function: \[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}. \] Rearranging this gives us: \[ \text{hypotenuse} = \frac{\text{opposite}}{\sin(\theta)}. \]
Plugging in the values:
- \(\theta = 12^\circ\),
- \(\text{opposite} = 1,000\) feet.
Now calculate the hypotenuse: \[ d = \frac{1000}{\sin(12^\circ)}. \]
Using a calculator to find \(\sin(12^\circ)\): \[ \sin(12^\circ) \approx 0.2079. \]
Now we can calculate: \[ d = \frac{1000}{0.2079} \approx 4810.9. \]
Rounding to the nearest foot, the distance the plane still needs to fly to reach the ground is approximately \(4811\) feet.
So, from the choices provided: 4810 is the closest answer.
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