An astronaut is working on a satellite 4200 miles above the ground. What is the measure of arc BD, the portion of earth that the astronaut can see? Round your answer to the nearest tenth. (earth's radius is approximately 4000 miles)

The distance from the shuttle to the horizon is 7158.2 miles

Step-by-step explanation:

the portion of earth that the astronaut can see is the distance from the shuttle to the horizon (d)

The earth radius is 4000 miles and the satellite is 4200 miles. This can be represented by a triangle with sides 4000 miles and d and a hypotenuse of (4000 + 4200 = 8200 miles). Using Pythagoras rule:

8200² = 4000² + d²

d² = 8200² - 4000²

d² = 51240000

d = 7158.2 miles

The distance from the shuttle to the horizon is 7158.2 miles