Question

An airplane is descending onto a runway. If the airplane is making a 12° angle with the horizontal line and its altitude is 500 feet, what is the horizontal distance between the airplane and the point it reaches the ground? Round the answer to the nearest foot.

(1 point)
Responses

2,405 feet
2,405 feet

932 feet
932 feet

2,352 feet
2,352 feet

511 feet

Answer 1

To find the horizontal distance between the airplane and the point it reaches the ground, we can use the trigonometric relationship of right triangles. We can use the tangent function, which relates the angle of descent, the altitude, and the horizontal distance.

Given:
- Angle of descent (θ) = 12°
- Altitude (h) = 500 feet

The tangent of the angle is given by:

\[
\tan(θ) = \frac{\text{opposite side}}{\text{adjacent side}} = \frac{\text{altitude}}{\text{horizontal distance}}
\]

Let's denote:
- Horizontal distance = \( d \)

So the equation becomes:

\[
\tan(12°) = \frac{500}{d}
\]

Now we solve for \( d \):

\[
d = \frac{500}{\tan(12°)}
\]

We can calculate \( \tan(12°) \):

\[
\tan(12°) \approx 0.2126
\]

Now, substituting this value into the equation:

\[
d = \frac{500}{0.2126} \approx 2355.4
\]

Rounding to the nearest foot, the horizontal distance \( d \approx 2355 \) feet.

Among the options provided, the closest available answer is:

**2,352 feet**