Question

A satellite is in orbit 600 km above Earth's surface. Earth's radius is about 6370 km. Using the Pythagorean Theorem, the distance (x) from the satellite to Earth's horizon is ______ km.What is the km? round the answer to the nearest whole number.

Answer 1

2829.13 km.

Step-by-step explanation:

If the radius of the Earth is 6370 km, the distance of the segment CD is also 6370 km.

Then, the sides of the rigth triangle are:

CB = 6370 km

AC = AD + DC

AC = 600 km + 6370 km

AC = 6970 km

AB = x

So, using the Pythagorean theorem we can calculate the value of x as follows:

`\begin{gathered} AB=\sqrt[]{(AC)^2-(CB)^2} \\ x=\sqrt[\square]{6970^2-6370^2} \end{gathered}`

Because AC is the hypotenuse and CB is on the legs of the triangle.

Therefore, solving for x, we get:

`x=2829.13\text{ km}`

Then, the answer is:

The distance (x) from the satellite to Earth's horizon is 2829.13 km.