In ancient times, it could be difficult to determine distances, especially for unreachable areas. For example, observers standing on a dock would have difficulty determining the distance to a ship. However with the application of trigonometry they were able to determine how far away the ship was.

The two observers stood at a set distance $d\={d}_{1}\+{d}_{2}$ from each other. They then used their instruments to measure the angles ${\mathrm{\theta}}_{1}and{\mathrm{\theta}}_{2}$to the boat. Now, the tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side, in this case:

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Therefore we know that $dequals;\frac{L}{\mathrm{tan}{\mathrm{\theta}}_{1}}plus;\frac{L}{\mathrm{tan}{\mathrm{\theta}}_{2}}$, or solving for $L$ and simplifying, $L\=\frac{d\cdot \mathrm{sin}{\mathrm{\theta}}_{1}\cdot \mathrm{sin}{\mathrm{\theta}}_{2}}{\mathrm{sin}\left({\mathrm{\theta}}_{1}plus;{\mathrm{\theta}}_{2}\right)}period;$