Let the height of the balloon be h.
The problem is illustrated in the diagram below:
Notice that the distances form sides of a right triangle. Apply the Pythagorean theorem to the triangle:
[tex]h^2+16^2=20^2[/tex]
Solve the equation for h:
[tex]\begin{gathered} h^2+256=400 \\ \Rightarrow h^2=400-256 \\ \Rightarrow h^2=144 \\ \Rightarrow h=\sqrt{144}=12 \end{gathered}[/tex]
The balloon has risen to a height of 12m.
