Question

From a radar station, the angle of elevation of an approaching airplane is 32.5 degree. The horizontal distance between the plane and the radar station is 35.6km. How far is the plane from the radar station to the nearest tenth of a kilometer?

Answer 1

Answer: 42.21 km

Step-by-step explanation:

We can solve this using trigonometry, since we have the following data:

$\theta=32.5\°$ is the the angle of elevation

$d=35.6 km$ is the horizontal distance between the plane and the radar station

$x$ 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:

$cos\theta=\frac{d}{x}$ because $d$ is the adjacent side of the right triangle

$cos(32.5\°)=\frac{35.6 km}{x}$

Finding $x$:

$x=\frac{35.6 km}{cos(32.5\°)}$

$x=42.21 km$