A second possibility for Thales\' method is the following: Suppose Thales was at

Question

A second possibility for Thales' method is the following: Suppose Thales was atop a tower on the shore with an instrument made of a straight stick and a crosspiece AC that could be rotated to any desired angle and then would remain where it was put (Fig. 2. 28). Thales rotates AC until he sights the ship S, then turns and sights an object T on shore without moving the cross-piece. Show that delta AET delta AES and therefore that SE = ET. Second method Thales could have used to determine the distance to a ship at sea

Explanation / Answer

IN THE DIAGRAM WE HAVE

IN THE 2 TRIANGLES AET AND AES

ANGLE AET = 90 = ANGLE AES..............TOWER IS VERTICAL

AE = AE .......................COMMON SIDE

ANGLE TAE = ANGLE SAE ...........SINCE THE SIGHTING INSTRUMENT AC IS ROTATED AT THE SAME ANGLE WRT ITS AXIS OF ROTATION AE.

SO BY CONGRUENCE THEOREM OF RIGHT ANGLED TRIANGLES WE GET

AET IS CONGRUENT TO AES

HENCE

AE = ES

THUS BY MEASURING THE DISTANCE AE ASHORE ON LAND , HE CAN FIND THE DISTANCE OF SHIP FROM THE SHORE.

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