To approach the runway, a small plane must begin a 9°

Question

descent starting from a height of 1536 feet above the ground. To the nearest tenth, what is the horizontal distance the airplane is at the start of this approach? (hint: there are 5,280 feet in a mile) ignore the X on the diagram. You must convert feet to miles.

Answer 1

To solve this problem, we can use trigonometry. The angle of descent is given as 9 degrees, which is the same as taking the tangent of 9 degrees.

Let's call the horizontal distance the airplane is at the start of the approach "x" (in miles), and the height of the airplane above the ground "h" (in feet).

The tangent of the angle of descent is equal to the ratio of the opposite side (h) to the adjacent side (x). So we can set up the equation:

tan(9 degrees) = h / x

Solving for x, we get:

x = h / tan(9 degrees)

Plugging in the values, we have:

x = 1536 feet / tan(9 degrees)

Now we need to convert feet to miles, using the conversion factor of 1 mile = 5280 feet:

x = (1536 feet / 5280) miles / tan(9 degrees)

Using a calculator, we find that tan(9 degrees) is approximately 0.15838.

x = (1536 / 5280) / 0.15838 miles

Calculating this out, we get:

x ≈ 0.161 miles

So, to the nearest tenth, the horizontal distance the airplane is at the start of this approach is approximately 0.2 miles.