Question

To approach the runway, a pilot of a small plane must begin a 10° 10 ° descent starting from a height of 1983 feet above the ground. To the nearest tenth of a mile, how many miles from the runway is the airplane at the start of this approach?

Answer 1

2.2 miles.

Explanation:

Please find the attachment.

Let x be the distance between runway and the airplane, where plane start the approach.

We have been given that to approach the runway, a pilot of a small plane must begin a 10° descent starting from a height of 1983 feet above the ground.

We can see from our attachment that angle DAC is equal to angle BCA (by alternate interior angles).

Side length AB is opposite side and x is hypotenuse for our given angle. Since Sine represents the relation between the hypotenuse and opposite of right triangle, so we will use sine to find the length of x.

`\text{Sin}=\frac{\text{Opposite}}{\text{hypotenuse}}`

`\text{Sin}(10^o)=(1983)/(x)`

`x=\frac{1983}{\text{Sin}(10^o)}`

`x=(1983)/(0.173648177667)`

`x=11419.6418680692448271`

Since length of x is in feet, let us convert our answer into miles.

1 mile = 5280 feet.

Let us divide length of x by 5280 to get our answer in miles.

`11419.6418680692448271\text{ Feet}=\frac{11419.6418680692448271\text{ feet}}{\frac{5280\text{ feet}}{\text{miles}}}`

`11419.6418680692448271\text{ Feet}=\frac{11419.6418680692448271\text{ feet}}{5280}* \frac{\text{ miles}}{\text{ feet}}`

`11419.6418680692448271\text{ Feet}=(11419.6418680692448271)/(5280)* \text{ miles}`

`11419.6418680692448271\text{ Feet}=2.162810959\text{ miles}\approx 2.2\text{ miles}`

Therefore, the distance between the runway and the airplane where it start this approach is 2.2 miles.