Horizon

The top of a lighthouse is 19 m above the sea. How far away is an object just "on the horizon"? [Assume the Earth is a sphere of radius 6378.1 km.]

Correct answer:

x =  15.6 km

Step-by-step explanation:

$$\begin{gathered} R=6378.1km \\ h=19m=0.019km \\ (R+h{)}^2=R^2+x^2 \\ {x}^2=(R+h{)}^2-R^2 \\ {x}^2=R^2+2Rh+h^2-R^2 \\ {x}^2=2Rh+h^2 \\ x=\sqrt{2Rh+h^2}=15.6\text{km} \end{gathered}$$

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