Answer: 42.21 km
Step-by-step explanation:
We can solve this using trigonometry, since we have the following data:
[tex]\theta=32.5\°[/tex] is the the angle of elevation
[tex]d=35.6 km[/tex] is the horizontal distance between the plane and the radar station
[tex]x[/tex] is the hypotenuse of the right triangle formed between the radar station and the airplane
Now, the trigonometric function that will be used is cosine:
[tex]cos\theta=\frac{d}{x}[/tex] because [tex]d[/tex] is the adjacent side of the right triangle
[tex]cos(32.5\°)=\frac{35.6 km}{x}[/tex]
Finding [tex]x[/tex]:
[tex]x=\frac{35.6 km}{cos(32.5\°)}[/tex]
[tex]x=42.21 km[/tex]
