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• Conic section
  ...described in [[Cartesian coordinates]] by a [[polynomial]] [[equation]] of degree two or less. ...cutting plane makes an [[angle]] with an [[axis]] that is larger than the angle between the slant height and the axis.
  5 KB (891 words) - 01:14, 9 January 2023
• Geometry
  ...he intersection two [[ray]]s at their endpoints. It is measure in either [[degree]]s or [[radian]]s, though the less-common [[Système international|metric]]
  3 KB (393 words) - 07:59, 25 September 2020
• 2002 AMC 12A Problems
  Find the degree measure of an angle whose complement is 25% of its supplement. ...a right triangle with <math>\angle ACB</math> as its right angle, <math>m\angle ABC = 60^{\circ}</math>, and <math>AB = 10</math>. Let <math>P</math> be ra
  12 KB (1,792 words) - 13:06, 19 February 2020
• 2001 AMC 12 Problems
  ...1,4)</math>, and <math>E=(0,4)</math>. What is the probability that <math>\angle APB</math> is obtuse? A polynomial of degree four with leading coefficient 1 and integer coefficients has two real zeros
  13 KB (1,957 words) - 12:53, 24 January 2024
• 2002 AMC 12B Problems
  Let <math>v, w, x, y, </math> and <math>z</math> be the degree measures of the five angles of a pentagon. Suppose that <math>v < w < x < y Let <math>\triangle XOY</math> be a right-angled triangle with <math>\angle XOY = 90^{\circ}</math>. Let <math>M</math> and <math>N</math> be the midpo
  10 KB (1,547 words) - 04:20, 9 October 2022
• 2006 AMC 12A Problems/Problem 22
  ...probability of choosing a point is <math>1 / 2</math>, or if the total arc degree measures add up to <math>\frac{1}{2} \cdot 360^{\circ} = 180^{\circ}</math> ...an [[isosceles triangle]]: <math>\angle AOP = 15^{\circ}</math> and <math>\angle OAP = OAB - 60^{\circ} = \frac{180^{\circ}-30^{\circ}}{2} - 60^{\circ} = 15
  2 KB (343 words) - 15:39, 14 June 2023
• 2006 AMC 10A Problems/Problem 19
  How many non-[[similar]] triangles have angles whose degree measures are distinct positive integers in [[arithmetic progression]]? ...c{180}{3} = 60</math> degrees. The minimum possible value for the smallest angle is <math>1</math> and the highest possible is <math>59</math> (since the nu
  2 KB (259 words) - 03:10, 22 June 2023
• 2005 AIME II Problems/Problem 12
  ...E<BF </math> and <math> E </math> between <math> A </math> and <math> F, m\angle EOF =45^\circ, </math> and <math> EF=400. </math> Given that <math> BF=p+q\ ...math>). Then <math>\tan \angle EOG = \frac{x}{450}</math>, and <math>\tan \angle FOG = \frac{y}{450}</math>.
  13 KB (2,080 words) - 21:20, 11 December 2022
• 2004 AIME II Problems/Problem 1
  ...angle]] which contains the entire chord is <math>60 \cdot 2 = 120</math> [[degree]]s, so the area of the [[sector]] is <math>\frac{1}{3}r^2\pi</math>; the re
  2 KB (329 words) - 23:20, 4 July 2013
• 1984 AIME Problems
  ...circ</math> and <math>180^\circ</math> in the complex plane. Determine the degree measure of <math>\theta</math>. ...{ cm}^2</math>. These two faces meet each other at a <math>30^\circ</math> angle. Find the volume of the tetrahedron in <math>\mbox{cm}^3</math>.
  6 KB (933 words) - 01:15, 19 June 2022
• 2001 AIME I Problems
  ...</math> degrees and <math>45</math> degrees, respectively. The bisector of angle <math>A</math> intersects <math>\overline{BC}</math> at <math>T</math>, and ...where <math>d < 120.</math> The length of the chord of a <math>3d</math>-degree arc is <math>- m + \sqrt {n}</math> centimeters, where <math>m</math> and <
  7 KB (1,212 words) - 22:16, 17 December 2023
• 1983 AIME Problems/Problem 14
  ...must add up to <math>180^{\circ}</math>. By the [[Law of Cosines]], <math>\angle APB=\cos^{-1}\left(\frac{{-11}}{24}\right)</math>. Also, angles <math>QPA</ ...). In other words, since <math>\angle TP'N = 90^\circ</math>, then <math> \angle TPN = 90^\circ</math>.
  13 KB (2,149 words) - 18:44, 5 February 2024
• 2001 AIME I Problems/Problem 13
  ...where <math>d < 120.</math> The length of the chord of a <math>3d</math>-degree arc is <math>- m + \sqrt {n}</math> centimeters, where <math>m</math> and < ...of the chords, <math>AD</math> and <math>BC</math>, of the <math>2d</math>-degree arcs can be represented as <math>x + 20</math>, as given in the problem.
  3 KB (561 words) - 19:25, 27 November 2022
• 2000 AIME II Problems/Problem 15
  ...in(1)=\frac{1}{60}</math> in degrees, convert to radians and use the small angle approximation <math>\sin(x)=x</math>. Hence, <math>S=\sin(1)</math>, and our angle is <math>\boxed{001}</math>.
  3 KB (469 words) - 21:14, 7 July 2022
• 1959 IMO Problems/Problem 4
  ...> is <math>ab</math>, since <math>a</math> and <math>b</math> form a right angle. However, twice the area of the triangle is also the product of <math>c</m We denote the angle between <math>b</math> and <math>c</math> as <math>\alpha</math>. The prob
  6 KB (939 words) - 17:31, 15 July 2023
• Right angle
  ...ne]]s. The [[measure of an angle | measure]] of every right angle is 90 [[degree (geometry) | degrees]] or <math>\frac \pi 2</math> [[radian]]s. When drawin * [[Angle]]
  673 bytes (91 words) - 23:59, 11 June 2022
• Supplementary
  ...ementary if they sum to <math>\displaystyle \pi</math> [[radian]]s (180 [[degree (geometry) | degrees]]).
  263 bytes (39 words) - 11:02, 7 September 2006
• Angle
  ...ex]] of the angle, and the rays themselves are called the [[side]]s of the angle. ...If there is no ambiguity, this notation can be shortened to simply <math>\angle B</math>.
  3 KB (568 words) - 20:21, 21 June 2019
• Radian
  ...measurement for [[angle|angles]]. In a circle, the measure of a [[central angle]] in radians is the ratio of the length of the [[intercepted arc]] to the l ...the whole circumference of the circle. Thus, radians can be converted to [[Degree (geometry)|degrees]]: <math>2\pi\; rad=360^\circ\implies\pi \;rad=180^\circ
  540 bytes (83 words) - 18:30, 10 March 2014
• Degree
  * [[Degree (geometry)]], the degrees in an [[angle]]. * [[Degree (graph theory)]], the degree of a [[vertex]] in a [[graph (graph theory) | graph]].
  233 bytes (33 words) - 19:26, 30 January 2007

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