Question

From the top of a 100 ft air traffic control tower, an airplane is observed flying in at an angle of 32. If the airplane is 3000 feet away, what is the plane's altitude?

Answer 1

Answer: 1974.6

Step-by-step explanation:

Given

From the top of the air traffic control tower which is h=100 ft tall

The plane is observed at an angle of $32^{\circ}$

Horizontal distance is 3000 ft

As per the diagram, we can write

$\Rightarrow \tan 32^{\circ}=\dfrac{H}{3000}\\\\\Rightarrow H=3000\tan 32^{\circ}=1874.6\ ft$

So, the plane altitude from the ground is $H+100=1974.6\ ft$