Answer:
12
Step-by-step explanation:
In the right triangle ABC,
[tex]BC^2=CH\cdot AC.[/tex]
Thus,
[tex]BC^2=26\cdot 8=208,\\ \\BC=\sqrt{208}=4\sqrt{13}.[/tex]
In the right triangle BHC, by the Pythagorean theorem,
[tex]BC^2=BH^2+CH^2.[/tex]
Then
[tex]BH^2=BC^2-CH^2,\\ \\BH^2=(\sqrt{208})^2-8^2=208-64=144,\\ \\BH=12.[/tex]
