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 to the nearest hundredths (2 decimal places).



(1 point)
feet

Answer 1

To find the distance the plane still needs to fly to reach the ground, we can use the relationship of a right triangle formed by the altitude, distance to be traveled (which we want to find), and the angle of depression.

Given:
- Altitude (height) \(h = 1000\) feet
- Angle of depression \( \theta = 12^\circ \)

In this scenario, the altitude is the opposite side of the triangle, and the distance to the ground (the hypotenuse) is what we're solving for.

Using the sine function, which is defined as:

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]

We can rearrange this to solve for the hypotenuse:

\[
\text{hypotenuse} = \frac{\text{opposite}}{\sin(\theta)}
\]

Plugging in our values:

\[
\text{hypotenuse} = \frac{1000}{\sin(12^\circ)}
\]

Now, calculate \( \sin(12^\circ) \):

Using a calculator, \( \sin(12^\circ) \approx 0.2079 \).

Then:

\[
\text{hypotenuse} = \frac{1000}{0.2079} \approx 4811.67 \text{ feet}
\]

Thus, the distance the plane still needs to fly to reach the ground is approximately:

\[
\boxed{4811.67} \text{ feet}
\]