What is Angles: Definition and 907 Discussions

The Angles (Old English: Ængle, Engle; Latin: Angli; German: Angeln) were one of the main Germanic peoples who settled in Great Britain in the post-Roman period. They founded several kingdoms of the Heptarchy in Anglo-Saxon England, and their name is the root of the name England ("land of Ængle"). According to Tacitus, writing before their move to Britain, Angles lived alongside Langobards and Semnones in historical regions of Schleswig and Holstein, which are today part of southern Denmark and northern Germany (Schleswig-Holstein).

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  1. F

    A About the nodal line in defining Euler angles

    I hope someone can explain this to me. In the definition of Euler angles, the body-fixed-azimuthal angel γ is measured from the nodal line that defines the intersection of the body-fixed-XY plane and the space fixed-xy plane to the body-fixed-Y axis. This is the green line in this image from...
  2. I

    How are angles in molecules calculated?

    I understand how angles are calculated in compounds where an atom is bonded to 2, 3, 5, and 6 bonds (bond pair + lone pair). But how do they work out the angle of a compound where an atom has 4 bonds (i.e. methane), in this case the carbon atom, has a H-C-H angle of 109.5°
  3. I

    MHB From Altitudes to Angles to Sides

    I don't know where to start
  4. T

    Calculating Bragg Angles for X-Ray Scattering from Table Salt Crystal

    Homework Statement The Spacing between the Na and Cl atoms in table salt (NaCl) is ##d=2.82x10^{-10}m##, which was first deduced from Bragg scattering. For an experiment where X-rays of energy 20 eV are produced, what are the corresponding Bragg angles below ##90^{\circ}## for scattering from a...
  5. zexxa

    Calculating uncertainty with a set of angles

    Homework Statement Hi there, the issue I'm having right now is finding the right way to calculate uncertainties when trigonometric terms come in play. The question goes like this, we're given 2 sets of 5 angles in degrees, the incident angle (10.0, 20.0, 30.0, 40.0, 50.0) and the other is the...
  6. Const@ntine

    Comp Sci Fortran: Find a triangle's side, plus angles

    The statement: In every ABC triangle, the laws of sine (a/sinA = b/sinB = c/sinC) & cosine (c2 = a2 + b2 -2*a*b*cosC) are valid, where a, b & c are the sides opposite to A, B & C respectively. Write a program that calculates and prints on the computer's screen, the length of c, and also the...
  7. Z

    Comparing angles opposite radius of a circle

    Homework Statement In circle O , BC >CD Compare x & y (which is greater?) Homework Equations There are no eq. Rule: angle opposite larger side is larger The Attempt at a Solution In my view both triangles are isosceles triangle. So x & y should be equal because they are both opposite the...
  8. R

    Intro to Angled Forces and Vectors question?

    Homework Statement The 5.7 N weight is in equilibrium under the influence of the three forces acting on it. The F force acts from above on the left at an angle of α with the horizontal. The 5.2 N force acts from above on the right at an angle of 63◦ with the horizontal. The force 5.7 N acts...
  9. F

    Need help finding roots for a complex number using angles

    so i am starting with the equation x3 = √(3) - i first : change to a vector magnitude = √[ (√(3))2 + 12] = 2 and angle = tan-1( 1/√(3) ) = 30 degrees (in fourth quadrant) so i have a vector of 2 ∠ - 30 so i plot the vector on the graph and consider that : 1. the fundamental theorum of...
  10. haruspex

    Insights Can Angles be Assigned a Dimension? - Comments

    haruspex submitted a new PF Insights post Can Angles be Assigned a Dimension? Continue reading the Original PF Insights Post.
  11. C

    Swimming with current, velocity, angles

    Hi, I have a homework and I am not sure about some things. 1. Homework Statement Person A and person B are next to river. Velocity of river is 1 m/s. There is a person drowning 30 m from shore. He doesn´t move, because there is a something, which he can hold. People A and B are 40 far from...
  12. O

    A How do you KNOW the Euler (Tait) angles cover orienations

    Well, that question just about states my issue. We have a body and we rotate about, say, the 3-axis of its body frame. Then, we must do the next rotation about the 1 or 2 axis. Let me say we choose the 1-axis Then we have a choice: continue on to the 2 axis or repeat the 3 axis. One set is...
  13. W

    Can anyone explain this sun reflection in terms of angles?

    I'm trying to understand the physics of reflection to better draw objects. Normally, you see the reflection of a light source on metallic surfaces where the angle of incidence can equal the angle of reflection. This should reflect an image of the source that is approximately equal in size to how...
  14. M

    MHB Proving angles are equal in a triangle in a circle.

    hi can someone help me work this out. i think it has something to do with the exterior angle of a triangle is equal to the sum of the interior angles but i can't work it.
  15. parshyaa

    B Measurements of angles in circular method

    Why θ in radian equals arc/radius? I know that it can't be proved but there must be a explanation for this formula. How founder may have got this idea.
  16. T

    MHB Find unknown angles of a triangle

    Dear friends, I am unable to find out the unknown angles for the following triangle which I attached with this post. Angle BAD and angle BCD are the unknown angles need to be calculated. Given that lines AB=BC=CD and angle CDE = 108 degrees From my calculations: angle ADC = 180 - 108 = 72...
  17. D

    Particle collisions - a question on angles relative to beam

    Consider the case in which an incoming particle collides with stationary target particle producing new particles through the interaction. For example, $$e^{-}+e^{+}\rightarrow X+\bar{X}$$ My question is, why in general do the particles produced in such an interaction propagate outwards are...
  18. M

    MHB State the angles in terms of x , Circle theorems

    Problem O is the center of the circle and AB is the diameter of this circle , C & D are points on this circle , If $\angle CDB=x^\circ$ ,State the following angles in terms of $x$ $\angle CAB$ $\angle CBA$ Workings & what is known $OC=OB=OA$ radii of the same circle $\therefore \angle...
  19. C

    MHB Inscribed Angles to Identifying and Understanding

    I've been having trouble identifying these inscribed angles for a while. I know the theorem that goes with this topic but I'm unsure how it applies :c.
  20. CollinsArg

    B Trying to represent a written geometrical description

    I'm reading an old book about Thales (Greek geometry), and I can't understand what the next part means, and how to represent it graphically, could you help me? thanks: It begin stating that if you divide an equilateral traingle with a perpendicular from a vertex on the opposite side, it'll be...
  21. Powergade

    Why Are the Angles in a Minkowski Diagram Equal for Different Observers?

    1. Homework Statement In a diagram where I have two observers (one still (A) and one moving with a "v" velocity (B)), where the two parts disagre in the simultaneity of events, how can I prove that the angles of the B person axis that are put in the A person axis are equal. (/alpha=/beta , in...
  22. M

    MHB Geometry: proving two angles are equal

    can some one show me how to work this out
  23. B

    MHB Complementary & Supplementary Angles

    The m<P is three less than twice the measure of <Q. If <P and <Q are supplementary angles, find the measures of both angles. The m<B is two more than three times the measure of <C. If <B and <C are complementary angles, find the measures of both angles.
  24. B

    MHB Finding the Measures of Angles in a Linear Pair

    <1 and <2 form a linear pair. If m<1 = 5x + 9 and m<2 = 3x + 11, find the measures of both angles.
  25. AlexKud

    Force required to lift a platform (over the range of angles)

    Homework Statement Hi, this is not really an academic homework but it is something I'm trying to solve for my future project. I have a background in electrical engineering hence I'm having a hard time solving the forces problem. https://dl.dropboxusercontent.com/u/43124243/Force_problem.png...
  26. Evangeline101

    Applications of Trig: related acute angles, coordinate plane

    Homework Statement Homework Equations none The Attempt at a Solution Two possible locations on the coordinate axis for the terminal arm of angle A: Two possible values for the measure of angle A and the related acute angle: Can someone please tell me if I did this correctly?
  27. F

    Simplifying Exterior Angles in a Polygon

    Homework Statement Homework Equations sum interior angles (n-2)*180 angles of a quadrilateral: a+b+c=d = 360 [/B] The Attempt at a Solution What do you do with the exterior angle? 80+130+a+x=360
  28. F

    What is the measure of an isosceles triangle angle when given its base angles?

    Homework Statement Find x[/B] Homework Equations a+b+c=180 [/B]The Attempt at a Solution So RP=RQ, the base angles are x and (146-x), normally the base angles are the same but in this scenario they are different. x+146-x+?=180
  29. F

    What are the sizes of angles in a scalene triangle with given expressions?

    Homework Statement The three angles of a scalene triangle are x degrees, (x-12) degrees and (2x+6) degrees. What sizes are the angles?[/B] Homework Equations Triangle = a+b+c =180 Scalene = no equal size or angles[/B]The Attempt at a Solution So what do you do with (x-12) degrees and (2x+6)...
  30. C

    B For oscillations, why do we use angles in waves and oscillat

    For example, the term angular frequency, it units is radian per second. For phase, it is also measured in radians or degrees, why is that? Why is the math the same when you use angles to describe oscillations?
  31. F

    Angle properties: Angles centered at a point?

    Homework Statement Find what x is I don't understand what to do with (3x-23). Homework Equations Angles centered at a point: a+b+c+d=360 https://drtayeb.files.wordpress.com/2011/03/igcse-math-extended.pdf (here is a pdf of the textbook, Exercise 4A, 3i.)[/B]The Attempt at a Solution...
  32. Mr Davis 97

    B Proof that exterior angles of a triangle sum to 360

    So I am working on this simple proof, but am confused about the term "external angle." The problem says that if ##a##, ##b##, and ##c## are external angles to a triangle, then ##a + b + c = 360##. However, is seems that the vertex of each triangle has two possible external angles, since there...
  33. MickeyBlue

    Tension in two wires at unknown angles

    Homework Statement An object at rest is suspended from two strings (A and B) as shown in the diagram, with A shorter than B. The object pulls on the point O with a force of 20 N. Each of the strings also exerts a force on the Point O. The angle between the strings at O is 90o. Which of the...
  34. F

    I How does the angle γ change under inversion in Euler angles?

    The well known Euler angles (αβγ) are defined as in the image It is easy to see that under inversion α → π+α β → π-β but I cannot figure out how γ transforms under inversion. actually I am stuck at the question whether I should measure it from the same intersection line ON (thence γ →π+γ) or...
  35. RoboNerd

    Question about determining the angles of triangle given two vectors

    <<Mentor note: Missing template due to originally being posted elsewhere>> Hello everyone. I have the following problem: Determine the angles of a triangle where two sides of a triangle are formed by the vectors A = 3i -4j -k and B=4i -j + 3k I thought that I would find the third side being...
  36. X

    Initial Velocity and Energy Conservation for Disk Collision

    Homework Statement Disk P (inertia 0.41 kg ) moves at an unknown velocity across a low-friction horizontal surface and collides with disk Q (inertia 0.75 kg ), which is initially at rest. After the collision, the two (now slightly dented) disks move apart without spinning. Velocity information...
  37. E

    I Is this a Trigonometric Identity?

    I have encountered this equation: ##\cos^2 \gamma = \cos^2 \alpha \cdot \cos^2 \beta## According to the paper, this is a trigonometric identity, but this is the first time I have encountered this. The angles ##\alpha## and ##\beta## are somewhat similar to the components of the distance...
  38. Y

    Angles Formed by Vector î + ĵ + √2k̂

    Homework Statement the angles which[/B] î + ĵ + √2k̂ makes with x axis, y-axis and z axis are? The Attempt at a Solution the question is basically asking us what angle î + ĵ + √2k̂ makes with î + ĵ + k̂ right? So since √2 is just the magnitude i thought the answer would be 90, 90, 90 the...
  39. Samia qureshi

    How we know that these angles are equal ?

    https://fbcdn-sphotos-a-a.akamaihd.net/hphotos-ak-xpa1/v/t1.0-9/13529050_1033411326734648_2364124398862717743_n.jpg?oh=991ce9f095c712dd7789ce0819be581e&oe=58016FFA&__gda__=1475707536_89e5606d703064d4c1ccd2e87d665c1b are these alternate interior angle or exterior angle? is it just because of...
  40. kostoglotov

    Difference between phase angles

    Homework Statement [/B] imgur: http://i.imgur.com/9ktFGSs.pngHomework EquationsThe Attempt at a Solution [/B] I came up with both 150 and 210 as the difference between the phase angles. I chose 150. If you draw the vectors and compare their angles, the angular difference between them could...
  41. K

    I Different densities of the universe on different angles?

    Does anybody know of a resource that I could use to determine the density of the universe along a specific line of sight? (right ascension and declination)I am investigating inertial forces and looking to identify both the most and least dense directions in space and determine by how much they...
  42. H

    Sum of the angles of a spherical triangle

    Homework Statement What is the sum of the angles of a spherical triangle formed on the surface of a sphere of radius R? The triangle is formed by the intersections of the arcs of great circles. Let A be the area of the surface of the sphere enclosed by the triangle. This question is a...
  43. R

    I Body rates from Euler angles....

    Referring to slides 3-4 (page 2) of this link: https://www.princeton.edu/~stengel/MAE331Lecture9.pdf The author states the relationship between body rates [p q r] and Euler angle rates [φ_dot θ_dot ψ_dot]. I want to verify this but have been failing miserably... My reasoning: 1) p, q, and r...
  44. Random Stuffs

    Why does light reflect at exactly 180 degrees?

    I understand the molecular principles behind the reflection itself, however it presents many problems, such as the one above. If you could explain it as easily as you can, I would be grateful. :)
  45. OrangeDog

    What is the Theoretical Solution for Lift at High Angles of Attack for Airfoils?

    I need a reference for the exact solution for lift at high angles of attack, when an airfoil behaves like a flat plate. I am pretty sure the theoretical solution is CL = 2 sin(α)*cos(α) based on two papers I read on lift through 180 degrees angle of attack, but I can't find in any of my books...
  46. shintashi

    How do I calculate Phase Angles?

    So I got to the part of my math/engineering textbook on vectors and scalars, and I've got to calculate phase angles and voltage. I see this equation, and I've tried doing it different ways but I don't get correct answers. tanθ=XL−XC / XR Angle θ represents the phase angle between the current...
  47. prashant singh

    I Why degree measure of angles are further divided in min,sec

    Whats the relation between degree and time, is there any historical answer.
  48. T

    Double-slit problem with incident and refracted angles

    Homework Statement For the given configuration, the path difference between the 2 rays is given as δ=dsinθ1 - dsinθ2 Homework Equations Small angle approximation? The Attempt at a Solution I'm used to seeing a double-slit situation where only the exit angle is specified, and thus path...
  49. P

    I Angles between complex vectors

    So I was trying to learn how to find the angle between two complex 4-dimentional vectors. I came across this paper, http://arxiv.org/pdf/math/9904077.pdf which I found to be a little confusing and as a result not overly helpful. I was wondering if anyone could help at all? Many thanks in...
  50. W

    Compton Scattering; Relation between scattering angles

    Homework Statement Show that the scatter angles of the photon (θ) and electron (Φ) in the Compton effect are related by the relation: ##cot (θ/2 )=(1+\frac{hf}{mοC^2}) tan(Φ) ## Where f is the frequency of incident photon 2. The attempt at a solution I wrote down the equations of conservation...
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