Question

A rocket ascends vertically after being launched from a location that is midway between two ground-based tracking stations. When the rocket reaches an altitude of 4 kilometers, it is 5 kilometers from each of the tracking stations. Assuming that this is a locale where the terrain is flat, how far apart are the two tracking stations?

Answer 1

if you just want confirmation of your hard work, what did you get?

If you got stuck, how far did you get? Did you draw a diagram? I think you'll see some more 3-4-5 triangles there.

Answer 2

I'm just stuck. Don't know exactly where to start.

Answer 3

Can't even draw a diagram?

Draw a vertical line. That's the rocket's path.

Label the bottom of the line B and place point T up somewhere and label BT with the number "4" the rocket's height.

Now draw a horizontal line through B, and at distance "x" mark points L and R for the left and right stations.

Now draw the two slanting lines LT and RT of length 5.

Now look. You have two right triangles with vertical leg 4 and hypotenuse 5.

Since x^2 + 4^2 = 5^2,
x = 3

so the distance LR between the stations is 3+3.

Got it?