






The basic problem of trigonometry runs somewhat like this: You stand next to a wide river and need to know the distance across itsay to a tree on the other shore, marked on the drawing here by the letter C (for simplicity, let's ignore the 3rd dimension). How can this be done without actually crossing the river? The usual prescription is as follows. Stick two poles in the ground at points A and B, and with a tape measure or surveyor's chain measure the distance c between them ("the baseline"). 
 Then remove the pole at A and replace it with a surveyor's telescope like the one shown here ("theodolite"), having a plate divided into 360 degrees, marking the direction ("azimuth") in which the telescope is pointing. Sighting the telescope, first at the tree and then at pole B, you measure the angle A of the triangle ABC, equal to the difference between the numbers you have read from the azimuth plate.. Replace the pole, take your scope to point B and measure the angle B in the same way.
The length c of the baseline, and the two angles A and B, contain all there is to know about the triangle ABCenough, for instance, to construct a triangle of the same size and shape on some convenient open field. Trigonometry (trigon = triangle) was originally the art of deriving the missing information by pure calculation. Given enough information to define a triangle, trigonometry lets you calculate its remaining dimensions and angles. 
Note: The details about the discovery of Mt. Everest and the survey of India are taken from "Who Discovered Mount Everest?" by Parke A. Dickey, Eos (Transactions of the American Geophysical Union), vol 66, p. 697700, 8 October 1985. The article is reprinted on p. 5459 of History of Geophysics, Vol. 4, edited by C. Stewart Gillmor, published by the American Geophysical Union, 1990.
A very readable account, including the story of William Lambton, who founded that survey, can be found in "The Great Arc : The Dramatic Tale of How India Was Mapped and Everest Was Named" by John Keay, 160 pages hard cover, Harper and Collins, Sept. 2000.

Next Stop: #M8 How to tell Sines from Cosines
Author and Curator: Dr. David P. Stern
Mail to Dr.Stern: stargaze("at" symbol)phy6.org .
Last updated 25 November 2001 Edited 28 October 2016