Here is a mantra that I learned in Geometry class in high school. We were all very excited, as angles had been invented only a few years earlier:
In a 30-60 right triangle ... the side opposite the 30 is half the hypotenuse the side opposite the 60 is half the hypotenuse times the square root of three.
So the tangent of the 30 would be (opposite) / (adjacent) = (1/2h) / (1/2h√3) .
That's (1)/(√3) or (√3)/(3) .
L oo k a t t h e p i c t u re . t an 3 0 o = 2 a 3 2 a = 2 a : 2 a 3 = 2 a ⋅ a 3 2 = 3 1 ⋅ 3 3 = 3 3
The exact value of tan 3 0 ⟩ is 3 3 . This is derived from the properties of a 30-60-90 triangle, where the opposite and adjacent sides have specific ratios. Thus, we use the tangent definition to calculate the result accurately.
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