frac112sqrt3

The expression "frac112sqrt3" appears to be a mathematical representation involving fractions and square roots. Interpreted correctly, it can be understood as the fraction one divided by the product of two, and the square root of three, specifically written as (1/2) * √3.

In mathematical terms, (1/2) * √3 is an irrational number that approximates to 0.8660254. This value frequently appears in geometry, especially in the context of equilateral triangles and 30-60-90 right triangles. For example, in a 30-60-90 triangle, the length of the longer leg is equal to the hypotenuse multiplied by √3/2, or equivalently, (1/2) * √3 when the hypotenuse is normalized to 1.

The value (1/2) * √3 can also be expressed as a simplified radical form, where the multiplication of a rational number and an irrational radical is often used to articulate specific measurements in trigonometry and geometric constructions. Its decimal equivalent is approximately 0.866, making it useful in calculations involving angles of 30 degrees or related trigonometric functions like sine and cosine, where sin(60°) and cos(30°) are both equal to this value.

Understanding the expression in various contexts highlights its importance in mathematics, particularly in trigonometric ratios and geometric proofs. The notation underscores how irrational numbers like √3 are often combined with rational coefficients to represent precise ratios inherent in natural and geometric phenomena.