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Start with an equilateral triangle with all sides of length 2 units and all angles of 60 degrees. Draw the altitude from the apex (top vertex) to the base. Since this is an equilateral triangle, it is easy to show that this line bisects the base.

So now you have a right angled triangle, with a base of 1 and a hypotenuse of 2. Therefore, by Pythagoras, its vertical height is sqrt(3).


Then tan(60) = opposite side/adjacent side = sqrt(3)/1 = 1.7321


It is probably easier if you sketch the diagrams as you go along.

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Q: Why the tangent of 60 degrees is 1.7321?
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