Question

A plane is descending at a 12 degree 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. Use the sketchpad to draw a picture.
(Round to the nearest WHOLE NUMBER)

480
4810
4809
479

Answer 1

To find the distance the plane still needs to fly to reach the ground, you can use a right triangle where:

- The altitude of the plane (1,000 feet) is the vertical leg of the triangle.
- The distance the plane needs to fly is the hypotenuse of the right triangle.
- The angle of depression (12 degrees) is the angle between the horizontal line (the ground) and the hypotenuse.

Using the angle of depression, we can determine the relationship between the altitude and the hypotenuse using the sine function. The sine of an angle is equal to the opposite side over the hypotenuse:

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

In this case:

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

where \( d \) is the distance the plane still needs to fly. Rearranging the formula gives us:

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

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

\[
\sin(12^\circ) \approx 0.2079
\]

Now substituting the value of \( \sin(12^\circ) \) into the equation:

\[
d \approx \frac{1000}{0.2079} \approx 4810.55 \text{ feet}
\]

Rounding to the nearest whole number gives \( d \approx 4811 \).

However, let's review the multiple-choice options you provided:
- 480
- 4810
- 4809
- 479

The closest answer is **4810 feet**.

Thus, the distance the plane still needs to fly to reach the ground is **4810 feet**.