Question

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).....

Answer 1

To find the distance the plane still needs to fly to reach the ground while descending at a 12° angle of depression, we can use some basic trigonometry.

The situation can be visualized as a right triangle where:
- The altitude (vertical leg) is 1,000 feet.
- The angle of depression to the ground is 12°.
- The distance the plane still needs to travel to the ground is the hypotenuse of the triangle.

We can use the sine function, which relates the opposite side and the hypotenuse:

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

Here, "opposite" corresponds to the altitude (1,000 feet) and "hypotenuse" is the distance we’re looking for (\(d\)).

\[
\sin(12°) = \frac{1000}{d}
\]

Rearranging to solve for \(d\):

\[
d = \frac{1000}{\sin(12°)}
\]

Now we can calculate \(\sin(12°)\):

\[
\sin(12°) \approx 0.2079
\]

So, substituting this value back into the equation:

\[
d \approx \frac{1000}{0.2079} \approx 4813.82 \text{ feet}
\]

Thus, the distance the plane still needs to fly to reach the ground is approximately **4813.82 feet** rounded to two decimal places.