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For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°. This is called an "angle-based" right triangle. A "side-based" right triangle is one in which the lengths of the sides form ratios of whole numbers, such as 3 : 4 : 5, or of other special numbers such as the golden ratio.
Trigonometry (from Ancient Greek τρίγωνον (trígōnon) 'triangle' and μέτρον (métron) 'measure') [1] is a branch of mathematics concerned with relationships between angles and side lengths of triangles. In particular, the trigonometric functions relate the angles of a right triangle with ratios of its side lengths.
Two sides and the included angle (SAS, side-angle-side) Two sides and an angle not included between them (SSA), if the side length adjacent to the angle is shorter than the other side length. A side and the two angles adjacent to it (ASA) A side, the angle opposite to it and an angle adjacent to it (AAS).
The included angle for any two sides of a polygon is the internal angle between those two sides.) If and only if three pairs of corresponding sides of two triangles are all in the same proportion, then the triangles are similar. [b] Two triangles that are congruent have exactly the same size and shape. All pairs of congruent triangles are also ...
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).
Case 3: two sides and an opposite angle given (SSA). The sine rule gives C and then we have Case 7. There are either one or two solutions. Case 4: two angles and an included side given (ASA). The four-part cotangent formulae for sets (cBaC) and (BaCb) give c and b, then A follows from the sine rule. Case 5: two angles and an opposite side given ...
The (3, 5, 7) triangle and its multiples are the only triangles with a 120° angle and having integer sides in arithmetic progression. [39] The only integer triangle with area = semiperimeter [40] has sides (3, 4, 5). The only integer triangles with area = perimeter have sides [40] [41] (5, 12, 13), (6, 8, 10), (6, 25, 29), (7, 15, 20), and (9 ...
60° rhombus (2 triangles) (Blue) that can be matched with two of the green triangles; 30° Narrow rhombus (Beige) with the same side-length as the green triangle; 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 ...