Trigonometry: the Ratio √3/2 and Its Relationship to the Angle 60° in a Right Triangle.

√3/2

sin(π/3)

√3/2 is a fraction that represents a trigonometric ratio of a specific angle in a right triangle. The angle that has this ratio is 60°.

To understand this, let’s consider a right triangle with one angle of 60°. The opposite side of the angle is half the length of the hypotenuse and the adjacent side is √3/2 times the length of the hypotenuse. We can express this relationship using the trigonometric function of sine, cosine, and tangent.

sin(60°) = opposite/hypotenuse = √3/2

cos(60°) = adjacent/hypotenuse = 1/2

tan(60°) = opposite/adjacent = √3

So, √3/2 represents the sine of the angle 60°. It is a rational number, which means it can be written as a fraction in the form of a/b, where a and b are integers with no common factors. In this case, it cannot be simplified any further.

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