Question

Multiple choice!!!!!!!!!

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. To the nearest tenth of a mile, how many miles from the runway is the airplane at the start of this approach?


Question 3 options:

11,419.6 mi

2.2 mi

0.4 mi

2.1 mi

Answer 1

You have to find one angle of the triangle first, and since we know the angle of depression is 10 and adds up with one of the degrees to 90, we can subtract 10 from 90 to get 80. We can then use cosine to find the length of x. Since we want to find the distance in miles instead of feet we will have to convert our final answer, which rounds to 2.2 miles

Answer 2

Option B. 2.2 miles.

Explanation:

A pilot of a small plane must begin a 10° descent starting from a height of 1983 feet above the ground that is AB is the height of plane above the ground, AB= 1983 feet. and A is the point from where the pilot starts descent.

thus, ∠ACB = ∠DAC = 10°

We have to find the distance between the runway and the airplane where it start this approach that is we have to find length AC( in miles).

Let AC = x

Applying trigonometric ratio,

`SinC=(Perpendicular)/(Hypotenuse)`

Put the values into the formula

sin 10° =
`(1983)/(x)`

0.1737 =
`(1983)/(x)`

x =
`(1983)/(0.1737)`

x= 11419.64

The distance from the runway to the airplane is 11419.64 feet.

As we know 1 mile = 5280 feet

11419.64 feet =
`(11419.64)/(5280)`

= 2.16 miles ≈ 2.2 miles

Option B. 2.2 mi is the correct answer.