Thales is said to have invented a method of finding distances of ships from shor

Question

Thales is said to have invented a method of finding distances of ships from shore by use of the angle-side-angle theorem. Here is a possible method: Suppose A is a point on shore and 5 is a ship (Fig. 2. 27). Mea- sure the distance AC along a perpendicular to AS and bisect it at 5. Draw CE at right angles to AC and pick point E on it in a straight line with B and S. Show that Delta EBC = Delta SB A and therefore that SA = EC. One method Thales could have used to determine the distance to a ship at sea

Explanation / Answer

B bisects AC, thus: AB = BC

AC and ES are crossing lines, thus angles SBA and CBE are equal.

On the other hand angles SAB and BCE are both equal to 90 degrees.

Therefore the two triangles SAB and BCE are equal, because they have two equal angles and one equal side.

So we have:

SA = EC

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