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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).
With the invention of the metric system, based on powers of ten, there was an attempt to replace degrees by decimal "degrees" in France and nearby countries, [note 3] where the number in a right angle is equal to 100 gon with 400 gon in a full circle (1° = 10 ⁄ 9 gon). This was called grade (nouveau) or grad.
The straight lines which form right angles are called perpendicular. [8] Euclid uses right angles in definitions 11 and 12 to define acute angles (those smaller than a right angle) and obtuse angles (those greater than a right angle). [9] Two angles are called complementary if their sum is a right angle. [10]
an object of diameter 1 AU (149 597 871 km) at a distance of 1 parsec (pc) Thus, the angular diameter of Earth's orbit around the Sun as viewed from a distance of 1 pc is 2″, as 1 AU is the mean radius of Earth's orbit. The angular diameter of the Sun, from a distance of one light-year, is 0.03″, and that of Earth 0.0003″. The angular ...
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.
In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle. Thales's theorem is a special case of the inscribed angle theorem and is mentioned and proved as part of the 31st proposition in the third book of Euclid 's Elements . [ 1 ]
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Since no triangle can have two obtuse angles, γ is an acute angle and the solution γ = arcsin D is unique. If b < c, the angle γ may be acute: γ = arcsin D or obtuse: γ ′ = 180° − γ. The figure on right shows the point C, the side b and the angle γ as the first solution, and the point C ′, side b ′ and the angle γ ′ as the ...