Question

1 fill in the blank 1 point
t.1.2
an airplane climbs at an angle of $12^{\circ}$ with the ground. find the horizontal distance the airplane has traveled once it has reached an altitude of 500 meters. round to the nearest tenth if needed.
the airplane will have traveled ______ meters.

Explanation:

Step1: Define trigonometric relationship

We use the tangent function: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$, where $\theta=12^\circ$, opposite side = 500 m (altitude), adjacent side = horizontal distance $x$.

Step2: Rearrange to solve for $x$

$x = \frac{500}{\tan(12^\circ)}$

Step3: Calculate the value

First, find $\tan(12^\circ) \approx 0.2126$. Then $x \approx \frac{500}{0.2126} \approx 2351.8$

Answer:

2351.8