Right triangle 30°-60°-90°

The right triangle with angles $30°$, $60°$, $90°$ is half of an equilateral triangle: this is where its characteristic ratios between the sides come from.

Theorem — 30°-60°-90° triangle

In a right triangle in which one leg is half the hypotenuse, the acute angles measure $30°$ and $60°$, and the other leg measures the first leg times $\sqrt{3}$: $\text{se } c = \frac{\text{ip}}{2} \quad\implies\quad c' = c\sqrt{3}, \quad \alpha = 30°, \quad \beta = 60°.$

The leg $c$ is half the hypotenuse $2c$; the other leg equals $c\sqrt{3}$.

Links

Topics: Euclidean circle
Concepts: Right triangle
Skills: Using formulae