Question

to approach the runway, a pilot of a small plane must begin a 10 degree descent from a height of 1790 feet above the ground. To the nearest tenth of a mile, how many miles away from the runway is the airplane at the start of this approach?

Answer 1

2.0 miles is the answer

Answer 2

Answer:

2.0 miles.

Step-by-step explanation:

Let x be the distance from the runway and airplane at the start of this approach.

We have been given that to approach the runway, a pilot of a small plane must begin a 10 degree descent from a height of 1790 feet above the ground.

We will use sine to solve our given problem as sine relates opposite side of a right triangle to its hypotenuse.

$\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}$

Upon substituting our given values in above formula, we will get:

$\text{sin}(10^{\circ})=\frac{1790}{x}$

$x=\frac{1790}{\text{sin}(10^{\circ})}$

$x=\frac{1790}{0.173648177667}$

$x=10308.1991648$

To convert the distance into miles, we will divide our distance in feet by 5280 as one mile equals to 5280 feet.

$x=\frac{10308.1991648}{5280}$

$x=1.95231044788$

Upon rounding our answer to the nearest tenth of a mile we will get,

$x\approx 2.0$

Therefore, the airplane is approximately 2.0 miles away from the runway at the start of this approach.