You fly a hot air balloon 1.5 miles above the ground. What is the measure of BD⌢, the portion of Earth that you can see? Round your answer to the nearest tenth. (Earth's radius is approximately 4000 miles.)

If the radius of the earth is R and the distance of the observer from the earth's surface is d, then the percent of the sphere's surface A that is visible to the observer is given by:[tex]A= \frac{50\%}{1+ \frac{R}{d} } [/tex]
Given that the hot balloon is 1.5 miles above the ground and that the radius of the earth is approximately 4000 miles, then the percent of the earth's surface that you can see is given by:[tex]A= \frac{50\%}{1+ \frac{4000}{1.5} } \\ \\ = \frac{50\%}{1+2666.67} \\ \\ = \frac{50\%}{2667.67} =0.0187\%[/tex]
Therefore, the measure of arc BD, the portion of Earth that you can see is 0.0187% of 360 degrees = 0.1 degrees.