Since both triangles are similar, the following relationship must be fulfilled:
[tex]\frac{x}{5.5ft}=\frac{10ft}{4ft}[/tex]
because 6 inches are equal to 0.5 feet. Then, by multiplying both sides by 5.5ft, we have
[tex]\begin{gathered} x=5.5ft\times\frac{10ft}{4ft} \\ x=\frac{55}{4}ft \\ x=13.75\text{ ft} \end{gathered}[/tex]
Therefore, the height of the lighthouse is 13.75 ft.
In order to express the result in feet and inches, lets convert 0.75 feet to inches. It yields,
[tex]\begin{gathered} 0.75ft=0.75ft(\frac{12in}{1ft}) \\ 0.75ft=0.75\times12\text{ in} \\ 0.75ft=9\text{ inches} \end{gathered}[/tex]
Then, another expression for the answer is 13 feet and 9 inches
