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 the answer to the nearest foot.

Answer 1

To find the distance the plane still needs to fly to reach the ground while descending at a 12° angle of depression from an altitude of 1,000 feet, we can use trigonometry. Specifically, we can use the tangent function, which relates the angle of depression to the opposite side (altitude) and the adjacent side (horizontal distance).

Given:
- Angle of depression (θ) = 12°
- Altitude (opposite side) = 1,000 feet

Using the tangent function:

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

Rearranging gives us:

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

Substituting the known values:

\[
\text{adjacent} = \frac{1000}{\tan(12°)}
\]

First, we'll calculate \(\tan(12°)\):

\[
\tan(12°) \approx 0.2126
\]

Now substituting this value into the equation:

\[
\text{adjacent} = \frac{1000}{0.2126} \approx 4691.3 \text{ feet}
\]

So, the distance the plane still needs to fly (the horizontal leg of the triangle) is approximately 4691.3 feet. Rounding to the nearest foot gives:

\[
\text{Distance} \approx 4691 \text{ feet}
\]

Thus, the plane still needs to fly approximately **4,691 feet** to reach the ground.