A plane is descending at a 12°

12
°
angle of depression. If the current altitude of the plane is 1,000 feet, find the distance the plane still needs to fly to reach the ground. Round the answer to the nearest foot.

1 answer

To find the horizontal distance \(d\) that a plane needs to fly to reach the ground while descending at a 12° angle, given its altitude of 1,000 feet, we can use trigonometry.

In this scenario, we can consider a right triangle where:

  • The altitude (height) of the plane is the opposite side \(h = 1000\) feet.
  • The angle of depression is \(12°\).
  • The distance \(d\) is the adjacent side.

Using the tangent function, which relates the opposite side to the adjacent side in a right triangle:

\[ \tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}} \]

We can set up the equation:

\[ \tan(12°) = \frac{1000}{d} \]

To find \(d\), we rearrange the equation:

\[ d = \frac{1000}{\tan(12°)} \]

Next, we need to calculate \(\tan(12°)\). Using a calculator:

\[ \tan(12°) \approx 0.2126 \]

Substituting this value into the equation gives:

\[ d = \frac{1000}{0.2126} \approx 4706.27 \]

Rounding to the nearest foot, the distance the plane still needs to fly to reach the ground is:

\[ \boxed{4706} \text{ feet} \]