earth has a radius of 3959 miles. a pilot is flying at a steady altitude of 1.8 miles above the earths…

Explanation:

Step1: Determine the radius to the pilot

The radius from the center of the Earth to the pilot is the sum of the Earth's radius and the pilot's altitude. Let $R = 3959$ miles (Earth - radius) and $h=1.8$ miles (altitude). The distance from the center of the Earth to the pilot $r=R + h=3959+1.8 = 3960.8$ miles.

Step2: Use the Pythagorean theorem

The line of sight from the pilot to the horizon, the radius of the Earth at the horizon - point, and the line from the center of the Earth to the pilot form a right - triangle. The radius of the Earth at the horizon - point is $R$, the distance from the center of the Earth to the pilot is $r$, and the distance from the pilot to the horizon is $d$. According to the Pythagorean theorem $d=\sqrt{r^{2}-R^{2}}$. Substitute $r = 3960.8$ miles and $R = 3959$ miles into the formula: [ \begin{align*} d&=\sqrt{(3960.8)^{2}-(3959)^{2}}\ &=\sqrt{(3960.8 + 3959)(3960.8-3959)}\ &=\sqrt{(7919.8)\times(1.8)}\ &=\sqrt{14255.64}\ &\approx119.4 \end{align*} ]

Answer:

$119.4$