Question

A plane is descending 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. (10 points)
feet



*Hint: Your number must be written correctly. This means numbers over 1,000 must have comma!

Answer 1

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

The situation describes a right triangle where:
- The altitude (vertical height) of the plane is the opposite side.
- The distance the plane still needs to fly is the hypotenuse of the triangle.
- The angle of depression from the horizontal is 12°.

Using the sine function, which relates the opposite side to the hypotenuse in a right triangle, we can write the following equation:

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

Where:
- \(\theta = 12°\)
- opposite = 1,000 feet (the altitude)
- hypotenuse = the distance we want to find (let's call it \(d\))

Rearranging the formula gives us:

\[
d = \frac{\text{opposite}}{\sin(\theta)} = \frac{1000}{\sin(12°)}
\]

Now, we need to calculate \(\sin(12°)\):

Using a calculator:

\[
\sin(12°) \approx 0.2079
\]

Now substituting this value into the equation for \(d\):

\[
d = \frac{1000}{0.2079} \approx 4811.65 \text{ feet}
\]

Rounding to the nearest foot:

\[
d \approx 4812 \text{ feet}
\]

Thus, the distance the plane still needs to fly to reach the ground is approximately **4,812 feet**.