Given:
A figure with measurement is given.
Required:
Find the height of the silo.
Explanation:
The given figure is:
Use the geometric man theorem in the right triangle ABD.
[tex]\begin{gathered} \frac{AC}{BC}=\frac{CD}{AC} \\ AC^2=BC\times CD \end{gathered}[/tex][tex]\begin{gathered} CD=BD-BC \\ =BD-6 \end{gathered}[/tex]
Substitute the given values.
[tex]\begin{gathered} (10)^2=6\times(BD-6) \\ 100=6(BD-6) \\ (BD-6)=\frac{100}{6} \\ (BD-6)=\frac{50}{3} \end{gathered}[/tex][tex]\begin{gathered} BD=\frac{50}{3}+6 \\ =\frac{50+18}{3} \\ =\frac{68}{3} \\ =22.7\text{ ft} \\ \approx23\text{ ft} \end{gathered}[/tex]
Final Answer:
The height of the silo is approximately 23 ft.
