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 your answer to the nearest foot. (1 point)208 feet4705 feet4810 feet3604 feet

Explanation:

Step1: Define trigonometric relationship

The altitude is the opposite side to the angle of depression, and the flight distance is the hypotenuse of the right triangle. We use the sine function:
$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Rearrange for hypotenuse

Isolate the hypotenuse (flight distance $d$):
$d = \frac{\text{altitude}}{\sin(\theta)}$

Step3: Substitute values and calculate

Altitude = 1000 ft, $\theta = 12^\circ$:
$d = \frac{1000}{\sin(12^\circ)}$
$\sin(12^\circ) \approx 0.2079$, so $d \approx \frac{1000}{0.2079} \approx 4810$

Answer:

4810 feet