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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.
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.
A right triangle ABC with its right angle at C, hypotenuse c, and legs a and b,. A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular, forming a right angle (1 ⁄ 4 turn or 90 degrees).
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.
A black square represents the borders of the file. Inside, the triangle is depicted with all of its special angles. 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 ...
Rational triangle; Right triangle. 30-60-90 triangle; Isosceles right triangle; Kepler triangle; ... Degree 3: Folium of Descartes: Cissoid of Diocles: Conchoid of de ...
An alternative construction (also by Ailles) places a 30°–60°–90° triangle in the middle with sidelengths of , , and . Its legs are each the hypotenuse of a 45°–45°–90° triangle, one with legs of length 1 {\displaystyle 1} and one with legs of length 3 {\displaystyle {\sqrt {3}}} .
Trapezoid (half hexagon or 3 triangles) (Red) that can be matched with three of the green triangles; Regular Hexagon (6 triangles) (Yellow) that can be matched with six of the green triangles; Square (Orange) with the same side-length as the green triangle; All the angles are multiples of 30° (1/12 of a circle): 30° (1×), 60° (2×), 90° (3 ...