To find the distance the plane still needs to fly to reach the ground when descending at a 12° angle of depression, we can use some trigonometry.
We can visualize the situation as a right triangle:
- The altitude of the plane (1,000 feet) represents the opposite side of the triangle.
- The distance the plane needs to fly (d) along the descent represents the hypotenuse.
- The angle of depression (12°) is the angle between the horizontal line and the line along which the plane is flying.
To find the hypotenuse \(d\), we can use the sine function, which relates the opposite side and the hypotenuse in a right triangle:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
Here, \(\theta\) is the angle of depression (12°) and the opposite side is the altitude (1,000 feet). Thus, we rearrange this formula to find \(d\):
\[ d = \frac{\text{opposite}}{\sin(\theta)} = \frac{1000}{\sin(12°)} \]
Now we'll calculate \(\sin(12°)\):
\(\sin(12°) \approx 0.2079\)
Now substitute this value into the equation:
\[ d = \frac{1000}{0.2079} \approx 4810.65 \]
Rounding this to the nearest foot, we find:
\[ d \approx 4811 \text{ feet} \]
Therefore, the distance the plane still needs to fly to reach the ground is approximately 4811 feet.
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