"through 360° in 60 minutes or 6° per minute. where: where: The time is 5:24. The angle in degrees of the hour hand is: The angle in degrees of the minute hand is: The angle between the hands can be found using the following formula: where If the angle is greater than 180 degrees then subtract it from 360 degrees. The time is 2:20. The time is 10:16. The hour and minute hands are superimposed only when their angle is the same. 10:54., and 12:00. Clock angle problem Clock angle problems are a type of mathematical problem which involve finding"
"angle may be expressed in different units: Throughout history, carpenters and masons have known a quick way to confirm if an angle is a true ""right angle."" It is based on the most widely known Pythagorean triple (3, 4, 5) and so called the ""Rule of 3-4-5."" From the angle in question, running a straight line along one side exactly three units in length, and along the second side exactly four units in length, will create a hypotenuse (the longer line opposite the right angle that connects the two measured endpoints) of exactly 5 units in length. This measurement can"
"Right angle In geometry and trigonometry, a right angle is an angle of exactly 90° (degrees), corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles. The term is a calque of Latin ""angulus rectus""; here ""rectus"" means ""upright"", referring to the vertical perpendicular to a horizontal base line. Closely related and important geometrical concepts are perpendicular lines, meaning lines that form right angles at their point of intersection, and orthogonality, which is the property of forming right angles, usually applied"
"an angle is the line, half-line, or line segment that divides an angle of less than 180° into two equal angles. The ""exterior"" or ""external bisector"" is the line that divides the supplementary angle (of 180° minus the original angle), formed by one side forming the original angle and the extension of the other side, into two equal angles. To bisect an angle with straightedge and compass, one draws a circle whose center is the vertex. The circle meets the angle at two points: one on each leg. Using each of these points as a center, draw two circles of"
"Degree (angle) A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle, defined so that a full rotation is 360 degrees. It is not an SI unit, as the SI unit of angular measure is the radian, but it is mentioned in the SI brochure as an accepted unit. Because a full rotation equals 2 radians, one degree is equivalent to radians. The original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is"
"In modern terminology, angles would normally be measured in degrees or radians. Modern school textbooks often define separate figures called lines (infinite), rays (semi-infinite), and line segments (of finite length). Euclid, rather than discussing a ray as an object that extends to infinity in one direction, would normally use locutions such as ""if the line is extended to a sufficient length,"" although he occasionally referred to ""infinite lines"". A ""line"" in Euclid could be either straight or curved, and he used the more specific term ""straight line"" when necessary. The Bridge of Asses (""Pons Asinorum"") states that ""in isosceles triangles"
"Perpendicular In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees). The property extends to other related geometric objects. A line is said to be perpendicular to another line if the two lines intersect at a right angle. Explicitly, a first line is perpendicular to a second line if (1) the two lines meet; and (2) at the point of intersection the straight angle on one side of the first line is cut by the second line into two congruent angles. Perpendicularity can be shown to be"
"angle across to make a right angle with one side, the right angle triangle's hypotenuse is length one and the sides are of length and . From this the trigonometric function tangent of 60° equals , and the sine of 60° and the cosine of 30° both equal . The square root of 3 also appears in algebraic expressions for various other trigonometric constants, including the sines of 3°, 12°, 15°, 21°, 24°, 33°, 39°, 48°, 51°, 57°, 66°, 69°, 75°, 78°, 84°, and 87°. It is the distance between parallel sides of a regular hexagon with sides of length"
"is 90°, leaving the remaining angle to be 30°. Right triangles whose sides are of integer lengths, with the sides collectively known as Pythagorean triples, possess angles that cannot all be rational numbers of degrees. (This follows from Niven's theorem.) They are most useful in that they may be easily remembered and any multiple of the sides produces the same relationship. Using Euclid's formula for generating Pythagorean triples, the sides must be in the ratio where ""m"" and ""n"" are any positive integers such that . There are several Pythagorean triples which are well-known, including those with sides in the"
"Right triangle A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle). The relation between the sides and angles of a right triangle is the basis for trigonometry. The side opposite the right angle is called the ""hypotenuse"" (side ""c"" in the figure). The sides adjacent to the right angle are called ""legs"" (or ""catheti"", singular: ""cathetus""). Side ""a"" may be identified as the side ""adjacent to angle B"" and ""opposed to"" (or ""opposite"") ""angle A"", while side ""b"" is the side ""adjacent to"
"Right triangle A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle). The relation between the sides and angles of a right triangle is the basis for trigonometry. The side opposite the right angle is called the ""hypotenuse"" (side ""c"" in the figure). The sides adjacent to the right angle are called ""legs"" (or ""catheti"", singular: ""cathetus""). Side ""a"" may be identified as the side ""adjacent to angle B"" and ""opposed to"" (or ""opposite"") ""angle A"", while side ""b"" is the side ""adjacent to"
". The power of the point with respect to the circle is equal to both and . Therefore, which is the law of cosines. Using algebraic measures for line segments (allowing negative numbers as lengths of segments) the case of obtuse angle () and acute angle () can be treated simultaneously. By using the law of sines and knowing that the angles of a triangle must sum to 180 degrees, we have the following system of equations (the three unknowns are the angles): Then, by using the third equation of the system, we obtain a system of two equations in"
"be perfectly sharp, either, since it is a course. Traditionally the configuration of the triangle is an equilateral triangle (3 equal sides and 3 equal angles of 60 degrees) with a ratio of the windward leg to a reaching leg being 1:1. In that case the course length for the 9 legs described above is 9 times the length of the windward leg. The angle at each point of the triangle is 60 degrees. The windward leg is generally aligned with the average wind direction. Another configuration is a triangle with a right angle at the wing mark and 45"
"the angle is measured as long as each angle is measured in the same unit. One ""radian"" is the angle subtended by an arc of a circle that has the same length as the circle's radius. The radian is the derived quantity of angular measurement in the SI system. By definition, it is dimensionless, though it may be specified as ""rad"" to avoid ambiguity. Angles measured in degrees, are shown with the symbol °. Subdivisions of the degree are minute (symbol ', 1' = 1/60°) and second {symbol "", 1"" = 1/3600°}. An angle of 360° corresponds to the angle"
"this system. In most mathematical work beyond practical geometry, angles are typically measured in radians rather than degrees. This is for a variety of reasons; for example, the trigonometric functions have simpler and more ""natural"" properties when their arguments are expressed in radians. These considerations outweigh the convenient divisibility of the number 360. One complete turn (360°) is equal to 2"""" radians, so 180° is equal to radians, or equivalently, the degree is a mathematical constant: 1° = . The turn (or revolution, full circle, full rotation, cycle) is used in technology and science. One turn is equal to 360°."
"teaching simple addition and subtraction, especially involving negative numbers. In advanced mathematics, the expressions ""real number line"", or ""real line"" are typically used to indicate the above-mentioned concept that every point on a straight line corresponds to a single real number, and . A number line is usually represented as being horizontal, but in a Cartesian coordinate plane the vertical axis (y-axis) is also a number line. According to one convention, positive numbers always lie on the right side of zero, negative numbers always lie on the left side of zero, and arrowheads on both ends of the line are"
"to one of the knife edges, and equals the angle at which the blade is held. The total angle from one side to the other is called the ""included angle"" – on a symmetric double-ground edge (a wedge shape), the angle from one edge to the other is thus ""twice"" the edge angle. Typical edge angles are about 20° (making the included angle 40° on a double-ground edge). The edge angle for very sharp knives can be as little as 10 degrees (for a 20° included angle). Knives that require a tough edge (such as those that chop) may sharpen"
"angle are called complementary. Complementary angles are formed when a ray shares the same vertex and is pointed in a direction that is in between the two original rays that form the right angle. The number of rays in between the two original rays is infinite. Angles whose sum is a straight angle are supplementary. Supplementary angles are formed when a ray shares the same vertex and is pointed in a direction that is in between the two original rays that form the straight angle (180 degree angle). The number of rays in between the two original rays is infinite."
"the two vertices are orthogonal, there is no edge between the vertices. If the angle between the two roots is 120 degrees, we put one edge between the vertices. If the angle is 135 degrees, we put two edges, and if the angle is 150 degrees, we put three edges. (These four cases exhaust all possible angles between pairs of positive simple roots.) Finally, if there are any edges between a given pair of vertices, we decorate them with an arrow pointing from the vertex corresponding to the longer root to the vertex corresponding to the shorter one. (The arrow"
". It is approximately equal to one milliradian ( ). A mil measuring of a revolution originated in the imperial Russian army, where an equilateral chord was divided into tenths to give a circle of 600 units. This may be seen on a lining plane (an early device for aiming indirect fire artillery) dating from about 1900 in the St. Petersburg Museum of Artillery. Degree (angle) A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle, defined so that a full rotation is 360"
"consists of a beam, a graduated dial and a blade which is connected to a swivel plate (with Vernier scale) by thumb nut and clamp. When the edges of the beam and blade are parallel, a small mark on the swivel plate coincides with the zero line on the graduated dial. To measure an angle between the beam and the blade of 90° or less, the reading may be obtained direct from the graduation number on the dial indicated by the mark on the swivel plate. To measure an angle of over 90°, subtract the number of degrees as indicated"
"of what a right angle is, namely two straight lines intersecting to form two equal and adjacent angles. The straight lines which form right angles are called perpendicular. 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). Two angles are called complementary if their sum is a right angle. Book 1 Postulate 4 states that all right angles are equal, which allows Euclid to use a right angle as a unit to measure other angles with. Euclid's commentator Proclus gave a"
"both the length of the hypotenuse and the angle the hypotenuse makes with the base line (""c"" above) at the same time when given ""x"" and ""y"". The angle returned is normally given by atan2(""y"",""x""). Orthographic projections: By means of trigonometric ratios, one can obtain the value of two acute angles, formula_3 and formula_4, of the right triangle. Given the length of the hypotenuse formula_5 and of a cathetus formula_6, the ratio is: The trigonometric inverse function is: in which formula_9 is the angle opposite the cathetus formula_6. The adjacent angle of the catheti formula_6 is formula_3 = 90° –"
"angles is equal to 90°, adding up to a total of 270°. Specifically, on a sphere the sum of the angles of a triangle is where ""f"" is the fraction of the sphere's area which is enclosed by the triangle. For example, suppose that we draw a triangle on the Earth's surface with vertices at the North Pole, at a point on the equator at 0° longitude, and a point on the equator at 90° West longitude. The great circle line between the latter two points is the equator, and the great circle line between either of those points and"
"exemplified by the ""x, y"", and ""z"" axes of a three-dimensional Cartesian coordinate system. Perpendicular In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees). The property extends to other related geometric objects. A line is said to be perpendicular to another line if the two lines intersect at a right angle. Explicitly, a first line is perpendicular to a second line if (1) the two lines meet; and (2) at the point of intersection the straight angle on one side of the first line is cut"
"angles of any triangle add up to 180 degrees. The two acute angles therefore add up to 90 degrees: they are complementary angles. The shape of a triangle is completely determined, except for similarity, by the angles. Once the angles are known, the ratios of the sides are determined, regardless of the overall size of the triangle. If the length of one of the sides is known, the other two are determined. These ratios are given by the following trigonometric functions of the known angle ""A"", where ""a"", "" b"" and ""c"" refer to the lengths of the sides in"
"C, and ∠CAB to the anticlockwise (positive) angle from C to B. The names, intervals, and measured units are shown in a table below: When two straight lines intersect at a point, four angles are formed. Pairwise these angles are named according to their location relative to each other. A transversal is a line that intersects a pair of (often parallel) lines and is associated with ""alternate interior angles"", ""corresponding angles"", ""interior angles"", and ""exterior angles"". There are three special angle pairs which involve the summation of angles: The size of a geometric angle is usually characterized by the magnitude"
"the circumcenter is located on a side of the triangle, then the opposite angle is a right one. If the circumcenter is located inside the triangle, then the triangle is acute; if the circumcenter is located outside the triangle, then the triangle is obtuse. An altitude of a triangle is a straight line through a vertex and perpendicular to (i.e. forming a right angle with) the opposite side. This opposite side is called the ""base"" of the altitude, and the point where the altitude intersects the base (or its extension) is called the ""foot"" of the altitude. The length of"
"distinguished by left-handed fittings. In trigonometry and mathematics in general, plane angles are conventionally measured counterclockwise, starting with 0° or 0 radians pointing directly to the right (or east), and 90° pointing straight up (or north). However, in navigation, compass headings increase clockwise around the compass face, starting with 0° at the top of the compass (the northerly direction), with 90° to the right (east). A circle defined parametrically in a positive Cartesian plane by the equations and is traced counterclockwise as the angle ""t"" increases in value, from the right-most point at . An alternative formulation with sin and"
"of thumb approximations only. The angle between a line and a curve (mixed angle) or between two intersecting curves (curvilinear angle) is defined to be the angle between the tangents at the point of intersection. Various names (now rarely, if ever, used) have been given to particular cases:—""amphicyrtic"" (Gr. , on both sides, κυρτός, convex) or ""cissoidal"" (Gr. κισσός, ivy), biconvex; ""xystroidal"" or ""sistroidal"" (Gr. ξυστρίς, a tool for scraping), concavo-convex; ""amphicoelic"" (Gr. κοίλη, a hollow) or ""angulus lunularis"", biconcave. The ancient Greek mathematicians knew how to bisect an angle (divide it into two angles of equal measure) using only"
"Edge angle and included angle typically characterize a blade's grind. An edge angle is measured between a line lying in the plane of one of the edge's faces and a second line intersecting the back's centre contour, both lines lying in the same plane normal to the edge. The included angle is the sum of the edge angles. Ceteris paribus, the smaller the included angle, the sharper the blade and the more easily damaged its edge. An appropriate grind depends upon a blade's intended use and the material composing it. Knife manufacturers may offer the same blade with different grinds"
"Gradian The gradian is a unit of measurement of an angle, equivalent to formula_1 of a turn, formula_2 of a degree, or formula_3 of a radian. The gradian is defined as formula_4 of the right angle (in other words, there are 100 gradians in the right angle), which implies a full turn being 400 gradians. It is also known as gon (from Greek /""gōnía"" for angle), grad, or grade. In continental Europe, the French term ""centigrade"" was in use for one hundredth of a grad. This was one reason for the adoption of the term Celsius to replace centigrade as"
"made of wood or metal (usually brass) divided on its arc side into 90 equal parts or degrees. The 90 divisions are gathered in 18 groups of five degrees each and are generally numbered both ways from the ends of the arc. That is, one set of numbers begins at the left end of the arc and goes to 90 at the right end while the other set the zero is at the right and the 90 is at the left. This double numbering enables the instrument to measure either celestial altitude or zenith distance or both simultaneously. At the"