Question

use the image to answer the question.
a plane is taking off at an angle of \\( \theta = 12^{\circ} \\) from a horizontal runway. to the nearest foot, find the distance the plane has flown when its altitude is 500 feet from the ground.
(1 point)
\\( \square \\) feet

Explanation:

Step1: Define sine relationship

$\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}$
Here, $\theta=12^\circ$, opposite side = 300 feet (altitude), hypotenuse = distance flown ($d$).

Step2: Rearrange to solve for $d$

$d = \frac{300}{\sin(12^\circ)}$

Step3: Calculate value

First, $\sin(12^\circ) \approx 0.2079$, so $d \approx \frac{300}{0.2079} \approx 1443$

Answer:

1443 feet