Hello, xiukhung!
Four spheres of radius 10 are placed on a table so that each touches 2 others.
Another sphere is placed on top.
Find the height of the top of this fifth sphere above the table.
The centers of the four spheres form a square with side
It is units above the table.
The center of the fifth sphere forms a square-base pyramid.
All of its edges have length
We find that the height of this pyramid is
The top of the fifth sphere is units above the pyramid.
Hence, the top of that sphere is: . units high.
Answer: .
I'm not certain if I understand your question correctly.
If the attached image describes the situation completely then you'll get x by using the Sine function:
Solve for x.
By the way: If you have a new question use a new thread. Otherwise you risk that no member of the forum will realize that you need further assistance.