Answer:
C. 2.0 miles.
Step-by-step explanation:
Please find the attachment.
Let x represent the required distance.
We have been given that to approach the runway, a pilot of a small plane must begin a 20-degree descent starting from a height of 3,760 ft above the ground.
Upon looking at the attached image, we can see that plane forms an right triangle with respect to ground, where angle of depression is 20 degrees.
To solve for x, we will use tangent as it relates the opposite side of a right triangle to adjacent.
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
[tex]\text{tan}(20^{\circ})=\frac{3760}{x}[/tex]
[tex]x=\frac{3760}{\text{tan}(20^{\circ})}[/tex]
[tex]x=\frac{3760}{0.363970234266}[/tex]
[tex]x=10330.515097[/tex]
Since our given distance is in feet, so we will divide our answer by 5280.
[tex]x=\frac{10330.515097}{5280}[/tex]
[tex]x=1.9565\approx 2.0[/tex]
Therefore, the airplane is 2 miles away from the runway at the start of this approach.
