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Answer :
To find the angle the plane's path will make with the runway, we use tangents in a right triangle formed by the altitude and distance to the runway. By taking the arctan of the altitude over the distance (7 miles / 190 miles), the descent angle is approximately 2.11 degrees.
The student has asked for the angle a plane's path will make with the runway when descending towards it. The given information is that the altitude of the plane is 7 miles and it is 190 miles away from the runway. To find this angle, we can use trigonometry, specifically the tangent function which relates angles to the ratio of the opposite side over the adjacent side in a right triangle.
First, we identify the right triangle formed by the altitude of the plane, the distance from the runway, and the hypotenuse (which would be the plane's path towards the runway). The altitude is the opposite side, and the distance to the runway is the adjacent side from the angle of descent at the plane's location.
Using the formula:
tangent(angle) = opposite / adjacent
In this case:
tangent(angle) = altitude / distance to runway
tangent(angle) = 7 miles / 190 miles
Now, we'll find the angle by taking the arctangent of both sides:
angle = arctan(7 / 190)
Using a calculator, we can determine that the angle is approximately:
angle ≈ 2.11 degrees
So, the plane's path will make an angle of approximately 2.11 degrees with the runway.
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Rewritten by : Barada
height = 7 miles, base dimension is 190 miles
to find the angle on the ground up to the plane
use arctan(7/190)
acrtan on a calculator is tan^-1
arctan(7/190) = 2.1099 degrees. Round off as necessary
