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 from each other. They then used their instruments to measure the angles 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:
Therefore we know that , or solving for and simplifying,