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An obtuse triangle (or obtuse-angled triangle) is a triangle with one obtuse angle (greater than 90°) and two acute angles. Since a triangle's angles must sum to 180° in Euclidean geometry , no Euclidean triangle can have more than one obtuse angle.
An angle larger than a right angle and smaller than a straight angle (between 90° and 180°) is called an obtuse angle [11] ("obtuse" meaning "blunt"). An angle equal to 1 / 2 turn (180° or π radians) is called a straight angle. [10] An angle larger than a straight angle but less than 1 turn (between 180° and 360°) is called a ...
Fig. 7a – Proof of the law of cosines for acute angle γ by "cutting and pasting". Fig. 7b – Proof of the law of cosines for obtuse angle γ by "cutting and pasting". One can also prove the law of cosines by calculating areas. The change of sign as the angle γ becomes obtuse makes a case distinction necessary. Recall that
Whether an isosceles triangle is acute, right or obtuse depends only on the angle at its apex. In Euclidean geometry, the base angles can not be obtuse (greater than 90°) or right (equal to 90°) because their measures would sum to at least 180°, the total of all angles in any Euclidean triangle. [9]
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 ...
The summit angles of a Saccheri quadrilateral are acute if the geometry is hyperbolic, right angles if the geometry is Euclidean and obtuse angles if the geometry is elliptic. The sum of the measures of the angles of any triangle is less than 180° if the geometry is hyperbolic, equal to 180° if the geometry is Euclidean, and greater than 180 ...
In hyperbolic geometry the fourth angle is acute, in Euclidean geometry it is a right angle and in elliptic geometry it is an obtuse angle. A Lambert quadrilateral can be constructed from a Saccheri quadrilateral by joining the midpoints of the base and summit of the Saccheri quadrilateral.
An easy formula for these properties is that in any three points in any shape, there is a triangle formed. Triangle ABC (example) has 3 points, and therefore, three angles; angle A, angle B, and angle C. Angle A, B, and C will always, when put together, will form 360 degrees. So, ∠A + ∠B + ∠C = 360°