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The fourth angle of a Lambert quadrilateral is an obtuse angle in elliptic geometry. The summit angles of a Saccheri quadrilateral are obtuse in elliptic geometry. The sum of the measures of the angles of any triangle is greater than 180° if the geometry is elliptic. That is, the defect of a triangle is negative. [80]
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 ...
An angle smaller than a right angle (less than 90°) is called an acute angle [11] ("acute" meaning "sharp"). An angle equal to 1 / 4 turn (90° or π / 2 radians) is called a right angle. Two lines that form a right angle are said to be normal, orthogonal, or perpendicular. [12]
In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (coordinates) are required to determine the position of a point. Most commonly, it is the three-dimensional Euclidean space, that is, the Euclidean space of dimension three, which models physical space.
When the rays are lines of sight from an observer to two points in space, it is known as the apparent distance or apparent separation. Angular distance appears in mathematics (in particular geometry and trigonometry) and all natural sciences (e.g., kinematics, astronomy, and geophysics).
The quaternions q, r, and s are used to represent rotations with axes of rotation w′, u′, and v′, respectively, and angles of rotation 2a, 2b, and 2c, respectively. Because these are double angles, each of q, r, and s represents two applications of the rotation implied by an edge of the spherical triangle. From the definitions, it follows ...
For a plane, the two angles are called its strike (angle) and its dip (angle). A strike line is the intersection of a horizontal plane with the observed planar feature (and therefore a horizontal line), and the strike angle is the bearing of this line (that is, relative to geographic north or from magnetic north). The dip is the angle between a ...
In China, Pei Xiu (224–271) identified "measuring right angles and acute angles" as the fifth of his six principles for accurate map-making, necessary to accurately establish distances, [5] while Liu Hui (c. 263) gives a version of the calculation above, for measuring perpendicular distances to inaccessible places.