Search results

  • ...this coordinate form as an ordered <math>n</math>-tuple of numbers within angle brackets or parentheses, <math>(x\,\,y\,\,z\,\,...)</math>. The set of vect For vectors <math>\vec{v}</math> and <math>\vec{w}</math>, with angle <math>\theta</math> formed by them, <math>\|\vec{v}+\vec{w}\|^2=\|\vec{v}\|
    11 KB (1,876 words) - 18:01, 29 August 2024
  • ...th>, the '''argument''' <math>\arg z</math> is the measure of the [[signed angle]] the [[ray]] <math>\overrightarrow{0z}</math> makes with the positive [[re
    1 KB (188 words) - 19:59, 31 July 2020
  • ...G}{GA}=\frac{H'G}{GC} = \frac{1}{2}</math>, and they both share a vertical angle, they are similar by SAS similarity. Thus, <math>AH' \parallel OM \perp BC< Denote <math>\angle A = \alpha, \angle B = \beta, \angle C = \gamma</math>
    59 KB (10,203 words) - 03:47, 30 August 2023
  • Let <math>ABCD</math> be a rhombus with <math>\angle A = 60^\circ</math>, and <math>P</math> is the intersection of diagonals <m ...\frac{1}{2} - 1 + 0 = -\frac{1}{2}</math>, where <math>h_X</math> is the (signed) [[height]] of <math>X</math> to <math>AB</math>, scaled by the height of <
    4 KB (734 words) - 11:41, 18 August 2020
  • ...ath>AB=5</math>, <math>BC=7</math>, and <math>AC=3</math>. The bisector of angle <math>A</math> meets side <math>\overline{BC}</math> at <math>D</math> and ...CF=3x</math> for some <math>x</math>. By the LoC, it is easy to see <math>\angle{BAC}=120^\circ</math> so <math>(5x)^2+(3x)^2-2\cos{60^\circ}(5x)(3x)=49</ma
    15 KB (2,516 words) - 16:28, 17 September 2024
  • ...ore, <math>\triangle ACF \sim \triangle AED</math>, so <math>\angle ACF = \angle AED</math>. Thus, quadrilateral <math>CFED</math> is cyclic, and <math>M</m We will use signed lengths. WLOG let <math>AC = 4</math>, <math>AM = x</math>, and <math>AE =
    4 KB (656 words) - 16:26, 20 June 2019
  • ...<math>24</math>, <math>1814</math>. On what day of the week was the treaty signed? ...ame time Bob looks due west from his house and sees the same airplane. The angle of elevation of the airplane is <math>30^\circ</math> from Alice's position
    14 KB (2,037 words) - 18:09, 29 July 2023
  • ...>y</math>, and <math>\beta{}</math> be defined as shown. Notice that if we angle chase, the sides of the other parallelogram are the same, but if the angles ...een the two sides that we switched is at the point <math>(0,0)</math>, the angle bisector of that vertex is <math>y=0</math>, and the black side is in the p
    7 KB (1,337 words) - 01:08, 9 January 2024