The Hubble Space Telescope is orbiting Earth 600 km above Earth's surface. Earth's radius is about 6370 km. Use the Pythagorean Theorem to find he distance a from the telescope to Earth's horizon. Round your answer to the nearest ten kilometers.

b^2 = (6970)^2 - (6370)^2

= 8.004*10^6
b = 2829 km

Draw the figure. Note it is a right triangle, with hypotenuse of (Rearth+altitude), legs of Rearth, and of what you want to find.

There is a right trangle formed by points at the center of the Earth, the HST satellite and the point where a line from the satellite is tangent to the Earth. The hypotenuse (c) goes from the HST to the center of the Earth, and its length is 600 + 6370= 6970 km. The side that you want is

b^2 = c^2 - a^2, where a is the radius of the Earth.

To find the distance "a" from the telescope to Earth's horizon, we can use the Pythagorean Theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the Earth's radius (6370 km) forms the first side of the right-angled triangle. The distance from the telescope to the Earth's horizon (a) forms the hypotenuse, and the second side is the distance from the Earth's surface to the telescope (600 km).

Using the Pythagorean Theorem, we can express this as:

a² = (6370 km)² + (600 km)²

a² = 40576900 km² + 360000 km²

a² = 40936900 km²

To find "a", we need to take the square root of both sides:

√(a²) = √(40936900 km²)

a = √(40936900) km

Calculating this, we find that a ≈ 6396 km.

Therefore, the distance from the Hubble Space Telescope to Earth's horizon is approximately 6396 km (rounded to the nearest ten kilometers).