A plane is descending towards a runway in Chicago. The plane is flying at an altitude of 7 miles and is 190 miles from the runway, as measured from the ground. What angle will the plane's path make with the runway?

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.