Question

From point P on the ground, the angle of elevation of an airplane is 23º. The altitude of the plane is 1200 meters. What is the distance from point P to the airplane, to the nearest tenth of a meter?

Answer 1

The distance from point P to the airplane is equal to 3071.2 meters.

Why?

We can solve the problem using the following trigonometric relation:

$sin(\alpha )=\frac{y}{hypothenuse} \\\\sin(23\°)=\frac{altitute}{distance}$

Substituting and calculating, we have:

[tex]sin(23\°)=\frac{altitute}{distance}\\\\distance=\frac{1200m}{sin(23\°)}=3071.2m[/tex]

Hence, we have that the distance from point P to the airplane is equal to 3071.2 meters.

Have a nice day!