The basic problem of trigonometry is something like this:
is near a wide river and need to know the distance to the other side, say to the tree marked in the drawing by the letter C (for simplicity, ignore the 3 rd dimension). How to do it without crossing the river?
The usual way is as follows. Drive two stakes into the ground at points A and B and with a tape measure the distance c between them (the "base").
An old surveyor's telescope (theodolite).
Then remove the post from point A and replace it with a surveyor's telescope as the one shown here ("theodolite"), with a plate divided into 360 degrees, check the direction ("azimuth") that points the telescope. Pointing the telescope to the tree first and then to the pole B, measures the angle A of triangle ABC equal to the difference between the numbers that you have read the azimuth plate. Replace the post, move the theodolite to point B and measured in the same way the angle B.
length c of the base and the two angles A and B are all you need to know the triangle ABC, enough, for example, to build a triangle of the same shape and same size, in a more convenient place. Trigonometry (trigon = triangle) at first was the art of calculating the lost information by simple calculation. Given sufficient information to define a triangle, trigonometry is used to calculate the other dimensions and angles.
is near a wide river and need to know the distance to the other side, say to the tree marked in the drawing by the letter C (for simplicity, ignore the 3 rd dimension). How to do it without crossing the river?
The usual way is as follows. Drive two stakes into the ground at points A and B and with a tape measure the distance c between them (the "base").
An old surveyor's telescope (theodolite).
Then remove the post from point A and replace it with a surveyor's telescope as the one shown here ("theodolite"), with a plate divided into 360 degrees, check the direction ("azimuth") that points the telescope. Pointing the telescope to the tree first and then to the pole B, measures the angle A of triangle ABC equal to the difference between the numbers that you have read the azimuth plate. Replace the post, move the theodolite to point B and measured in the same way the angle B.
length c of the base and the two angles A and B are all you need to know the triangle ABC, enough, for example, to build a triangle of the same shape and same size, in a more convenient place. Trigonometry (trigon = triangle) at first was the art of calculating the lost information by simple calculation. Given sufficient information to define a triangle, trigonometry is used to calculate the other dimensions and angles.
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