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.

Answer 1

To solve this problem, we can use trigonometry. We can create a right triangle where:

- The altitude (height) of the plane is the opposite side (1000 feet).
- The distance the plane needs to fly to reach the ground is the adjacent side (which we'll calculate).
- The angle of depression is \(12^\circ\).

Using the tangent function, which relates the angle to the opposite and adjacent sides of a right triangle, we can express this relationship as:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]

In this case, we have:

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

where \(d\) is the distance the plane still needs to fly. Rearranging the equation to solve for \(d\):

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

Now, we will calculate \(\tan(12^\circ)\):

\[
\tan(12^\circ) \approx 0.2126 \quad (\text{using a calculator})
\]

Now substituting that into the equation for \(d\):

\[
d = \frac{1000}{0.2126} \approx 4691.25
\]

Rounding to the nearest foot, the distance the plane still needs to fly to reach the ground is:

\[
\boxed{4691 \text{ feet}}
\]