Trigonometry in Geology
An example of applied trigonometry in geology:
Look at the picture here on the left. Now we are about 20 kilometers (13 miles) North from the picture of the homepage and looking at the same two mountains but facing South...
On the right-hand side of the picture is Mount San Giorgio (the people swimming underneath are my children and my wife). On the left hand-side is Mount Generoso (a Mesozoic to Cenozoic oceanic deposit).
Mount San Giorgio is quite famous for his Triassic fossils and its geology is fairly well known.
Now we simplify the geology for educational purposes.
A geologist can measure the distance D of an outcropping strata and its inclination - which is the angle or "how steep" the layer is "going down" - (a geologist uses a simple geologist compass
which is alway equipped with a clinometer).
As we said, the real width or thickness of the strata W can be simply derived by fields measurement of D (using a meter or just by counting the footsteps) and Θ (using a geologist compass ).
In fact, trigonometry enshrine "secret" natural rules which bind those three units : W, D, Θ.
In other words, we can imagine that D and W are the sides of a right triangle, and Θ is one angle of it (see the picture below).
The Greek astronomers found out that the relation which binds those 3 things (D, W,Θ) in a right triangle is universal (i.d. valid in all universe, yes) and indipendent from the size of the triangle!
And the relation is:
Now, "sinΘ" is just an "intelligent proportion" - a number - going from 0 to 1.
From algebra, you will know that the above relation can also be written as
Now, let's say we measured Θ = 30º and D=50 meters, then we have
So the solution of our "trigonometry in geology" example is that the real strata is about 22,7 meters wide.
On the shore of a vast sea
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Stay in touch with nature. It's full of mathematics!
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