Question

An airplane climbs at an angle of 12 with the ground. Find the horizontal distance il has traveled once it has reached an altitude of 500 feel.

Answer 1

The situation given can be pictured as follows:

The altitude reached by the plane is the opposite leg of the angle of 12°, to find it we can use the tangent function, which is defined as:

$\tan \theta=\frac{\text{opp}}{\text{adj}}$

Plugging the values given we have that:

$\tan 12=\frac{x}{500}$

solving for x we have:

$\begin{gathered} \tan 12=\frac{x}{500} \\ x=500\tan 12 \\ x=106.2783 \end{gathered}$

Therefore the height of the plane is 106.2783 ft.