Aplane is flying at an altitude of 12000m from the pilot the angle of depression tothe airport toweris32 degrees how far is the tower from a point directly beneath the plane
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To find the distance from the tower to a point directly beneath the plane, we can use trigonometry. In this case, we have an angle of depression, which means the angle formed by the line of sight from the pilot to the tower and a horizontal line.
Let's break down the problem:
- The altitude of the plane is given as 12,000m.
- The angle of depression is given as 32 degrees.
We can visualize the situation as a right triangle. The altitude of the plane is the opposite side, and the distance from the tower to the point directly beneath the plane is the adjacent side.
Using the tangent function, we have the following equation:
tan(angle) = opposite/adjacent
In this case, we know the angle and the opposite side (altitude), and we need to calculate the adjacent side (distance to the tower).
So, the equation becomes:
tan(32°) = 12,000m / adjacent
To solve for the adjacent side (distance to the tower), we rearrange the equation:
adjacent = 12,000m / tan(32°)
Calculating the trigonometric function:
tan(32°) ≈ 0.6249 (approximate value)
Substituting in the values:
adjacent ≈ 12,000m / 0.6249
Using a calculator, we find:
adjacent ≈ 19,205.13m
Therefore, the tower is approximately 19,205.13 meters away from the point directly beneath the plane.