Question

A plane is descending at a 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. Type numbers only, no commas or letters.



(1 point)
feet

Answer 1

To find the horizontal distance the plane still needs to fly to reach the ground, we can use basic trigonometry.

Given:
- Angle of depression: 12°
- Altitude of the plane: 1,000 feet

We can use the tangent function, which relates the angle of depression, the opposite side (altitude), and the adjacent side (horizontal distance):

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

Where:
- \(\theta = 12°\)
- Opposite = altitude = 1,000 feet
- Adjacent = horizontal distance (distance we need to find)

Rearranging the formula gives us:

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

Substituting the known values:

\[
\text{adjacent} = \frac{1000}{\tan(12°)}
\]

Calculating \(\tan(12°)\) (using a calculator):

\[
\tan(12°) \approx 0.2126
\]

Now substitute back:

\[
\text{adjacent} = \frac{1000}{0.2126} \approx qualitatively}
\]

Calculating that gives:

\[
\text{adjacent} \approx 4691.36 \text{ feet}
\]

Rounding to the nearest foot:

**The distance the plane still needs to fly to reach the ground is approximately 4691 feet.**

So the answer is:

4691