A plane is flying at an altitude of 12,000 m. From the pilot, the angle of depression to the airport tower is 32°. How far is the tower from a point directly beneath the plane?

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I’m confused

To determine the distance from the tower to a point directly beneath the plane, we can use trigonometry.

Let's call the distance from the tower to the point directly beneath the plane "x".

In this scenario, we have an angle of depression of 32 degrees from the pilot to the airport tower. The angle of depression is the angle between the horizontal line and the line of sight downward from an observer to an object. Since this angle is given, we can use the tangent function to find the value of "x".

Tangent is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. In this case, the opposite side is 12,000 m (altitude), and the adjacent side is "x" (distance from the tower to the point beneath the plane).

So, we can write the equation as:

tan(32°) = opposite/adjacent
tan(32°) = 12,000/x

To solve for "x," we can rearrange the equation:

x = 12,000 / tan(32°)

Now, we can use a calculator to calculate the value of tan(32°) and then substitute it into the equation to find the value of "x".

After evaluating this expression, we find that "x" is approximately 15,925.52 meters.

Therefore, the tower is approximately 15,925.52 meters away from the point directly beneath the plane.

12000/x = sin 32°