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Then ABD is a 30°–60°–90° triangle with hypotenuse of length 2, and base BD of length 1. The fact that the remaining leg AD has length √ 3 follows immediately from the Pythagorean theorem. The 30°–60°–90° triangle is the only right triangle whose angles are in an arithmetic progression.
The values of sine and cosine of 30 and 60 degrees are derived by analysis of the equilateral triangle. In an equilateral triangle, the 3 angles are equal and sum to 180°, therefore each corner angle is 60°. Bisecting one corner, the special right triangle with angles 30-60-90 is obtained.
The right angle is symbolized by a small square, and its measure, 90°, is written to the right and above it. The angle placed to the right of the 90° angle is shown as an arc, and its measure, 30°, is written to the left of the arc. The angle above the right angle is also represented by an arc, and its measure, 60°, is written below said arc.
English: Diagram demonstrating the ratios of the sides of a 30-60-90 special right triangle. Français : DProportions entre le côté d'un triangle équilatéral et sa hauteur. The source code of this SVG is invalid due to 32 errors.
File:Bad drawing of a 30-60-90 triangle.svg. SVG development . The SVG code is . This trigonometry was created with a text editor. Licensing. Public ...
A woman who is 36–24–36 (91.5–61–91.5) at 5 ft 3 in (1.60 m) tall looks different from a woman who is 36–24–36 at 5 ft 8 in (1.73 m) tall. Since the latter woman's figure has greater distance between measuring points, she will likely appear thinner than her former counterpart, again, even though they share the same measurements.
A Semisextile or Duodecile is an angle of 30°, which is 1 ⁄ 12 of the 360° ecliptic. An orb of ±1.2° is allowed. The symbol is 1 ⁄ 2 a Sextile (60°), which is the top radii of a hexagon; the internal angles are 60°. Of the minor aspects, it may be the most often used, because it can be easily seen.
These set squares come in two usual forms, both right triangles: one with 90-45-45 degree angles, the other with 30-60-90 degree angles. Combining the two forms by placing the hypotenuses together will also yield 15° and 75° angles.