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?
Answers
Steve
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.
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.
Anonymous
I'm just stuck. Don't know exactly where to start.
Steve
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?
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?