Question

A sailor is standing next to a lighthouse. He places a mirror on the ground 10 feet from the lighthouse and walks backward until he can see the top in the mirror. He is 4 feet away from the mirror, and his eyes are 5 feet 6 inches above the ground. What is the height of the lighthouse?

Answer 1

Since both triangles are similar, the following relationship must be fulfilled:

`(x)/(5.5ft)=(10ft)/(4ft)`

because 6 inches are equal to 0.5 feet. Then, by multiplying both sides by 5.5ft, we have

`\begin{gathered} x=5.5ft*(10ft)/(4ft) \\ x=(55)/(4)ft \\ x=13.75\text{ ft} \end{gathered}`

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,

`\begin{gathered} 0.75ft=0.75ft((12in)/(1ft)) \\ 0.75ft=0.75*12\text{ in} \\ 0.75ft=9\text{ inches} \end{gathered}`

Then, another expression for the answer is 13 feet and 9 inches