Question

An airplane is descending at a 13°
angle of depression. Given that the current horizontal distance between the runway and the airplane is 2,300 feet, apply the sine ratio to find the current altitude of the airplane to the nearest foot.(1 point)

Answer 1

To find the altitude of the airplane using the sine ratio, we can relate the angle of depression, the altitude, and the horizontal distance.

When the airplane descends at a 13° angle of depression, this means that the angle between the horizontal line (the distance to the runway) and the line of descent (the hypotenuse) is 13°. Accordingly, we can denote:

- \( \theta = 13^\circ \) (the angle of depression, which corresponds to the angle in the right triangle)
- \( d = 2300 \) feet (the horizontal distance to the runway)
- \( h \) = altitude of the airplane (the opposite side of the triangle)

Using the sine ratio:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]

Since we want to find the altitude \( h \), we can express the relationship in terms of the sine of the angle:
\[
\sin(13^\circ) = \frac{h}{d}
\]
Thus, we can rearrange this to find \( h \):
\[
h = d \cdot \sin(13^\circ)
\]
Now, substituting the value of \( d \):
\[
h = 2300 \cdot \sin(13^\circ)
\]

Next, we calculate \( \sin(13^\circ) \):
Using a calculator, we find:
\[
\sin(13^\circ) \approx 0.224951
\]

Now, substituting this value back in:
\[
h \approx 2300 \cdot 0.224951 \approx 517.8
\]

Rounding to the nearest foot:
\[
h \approx 518 \text{ feet}
\]

Thus, the current altitude of the airplane is approximately **518 feet**.