AN AIRPLANE IS FLYING AT A HEIGHT OF 1000 m. THE ANGLE OF DEPRESSION OF AIRPORT A FROM THE PLANE IS 15°. CALCULATE THE HORIZONTAL DISTANCE BETWEEN THE AIRPLANE AND THE AIRPORT.
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Tan15 = 1000/d, d = ?
To calculate the horizontal distance between the airplane and the airport, we can use the tangent function.
The tangent of the angle of depression is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the airplane (1000 m) and the adjacent side is the horizontal distance we want to find (x).
So, we can use the equation: tan(15°) = 1000 m / x
To find x, we need to isolate it on one side of the equation.
First, divide both sides of the equation by tan(15°):
1000 m / tan(15°) = x
Now, let's calculate the value of x:
x ≈ 3640.787 m
Therefore, the horizontal distance between the airplane and the airport is approximately 3640.787 meters.
To find the horizontal distance between the airplane and the airport, we can use trigonometry. The angle of depression, in this case, is the angle between the horizontal line and the line of sight from the airplane to the airport.
We can visualize this situation with a right triangle. The vertical side represents the height of the airplane, which is 1000 m, and the angle of depression is 15°. The horizontal distance we want to find is the adjacent side to the angle.
Using trigonometric ratios, we know that the tangent of an angle is equal to the opposite side divided by the adjacent side.
In this case, the tangent of 15° is equal to the height of the airplane divided by the horizontal distance.
tan(15°) = opposite/adjacent
tan(15°) = 1000/adjacent
To find the horizontal distance, we rearrange the equation:
adjacent = opposite / tan(15°)
adjacent = 1000 / tan(15°)
Using a calculator, we can find the value of tan(15°) to be approximately 0.268.
adjacent = 1000 / 0.268
adjacent ≈ 3726.87 m
Therefore, the horizontal distance between the airplane and the airport is approximately 3726.87 meters.