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. (Hint: Draw it out)

a. 978 feet
b. 1122 feet
c. 4810 feet
d. 208 feet

Answer 1

To solve the problem, we can use basic trigonometry. Given the altitude of the plane (1,000 feet) and the angle of depression (12°), we can model the situation using a right triangle.

1. **Define the triangle**:
- The altitude of the plane represents the opposite side of the triangle (1,000 feet).
- The distance the plane needs to fly to reach the ground is the hypotenuse (let's denote this as \( d \)).
- The angle of depression (12°) corresponds to the angle of elevation from the ground to the plane.

2. **Use the sine function**:
Since we know the opposite side (altitude) and the angle, we can use the sine function, which relates opposite to hypotenuse:

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

Substituting the known values:

\[
\sin(12°) = \frac{1000}{d}
\]

3. **Rearranging the equation**:
To find \( d \), we can rearrange the equation:

\[
d = \frac{1000}{\sin(12°)}
\]

4. **Calculate \( \sin(12°) \)**:
Using a calculator, we find:

\[
\sin(12°) \approx 0.2079
\]

5. **Now substitute and calculate \( d \)**:

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

6. **Rounding the answer**:
Rounding to the nearest foot gives:

\[
d \approx 4811 \text{ feet}
\]

Hence, the closest option in the choices provided is:

**c. 4810 feet**