To approach the runway, a small plane must begin a 9°
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.
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.
To find the horizontal distance the airplane is at the start of the approach, we can use trigonometry. The horizontal distance can be found using the tangent function.
Tangent (θ) = Opposite / Adjacent
In this case, the angle of descent is 9° and the height (opposite side) is 1536 feet. We want to calculate the adjacent side which represents the horizontal distance.
Tangent (9°) = 1536 feet / Adjacent
Rearranging the equation, we get:
Adjacent = 1536 feet / Tangent (9°)
Calculating the tangent of 9°:
Tangent (9°) = 0.15838444
Now, we can substitute this value into the formula to calculate the adjacent side:
Adjacent = 1536 feet / 0.15838444
Calculating the result to the nearest tenth:
Adjacent ≈ 9707.3 feet
To convert feet to miles, divide the adjacent distance by 5280 feet (the number of feet in a mile):
Adjacent (in miles) = 9707.3 feet / 5280 feet
Calculating the result:
Adjacent (in miles) ≈ 1.84 miles
Therefore, to the nearest tenth, the horizontal distance the airplane is at the start of the approach is approximately 1.84 miles.