Answer:
The horizontal distance from the plane to the person on the runway is 20408.16 ft.
Step-by-step explanation:
Consider the figure below,
Where AB represent altitude of the plane is 4000 ft above the ground , C represents the runner. The angle of elevation from the runway to the plane is 11.1°
BC is the horizontal distance from the plane to the person on the runway.
We have to find distance BC,
Using trigonometric ratio,
[tex]\tan\theta=\frac{Perpendicular}{base}[/tex]
Here, [tex]\theta=11.1^{\circ}[/tex] ,Perpendicular AB = 4000
[tex]\tan\theta=\frac{AB}{BC}[/tex]
[tex]\tan 11.1^{\circ} =\frac{4000}{BC}[/tex]
Solving for BC, we get,
[tex]BC=\frac{4000}{\tan 11.1^{\circ} }[/tex]
[tex]BC=\frac{4000}{0.196}[/tex] (approx)
[tex]BC=20408.16[/tex](approx)
Thus, the horizontal distance from the plane to the person on the runway is 20408.16 ft
