What is Angles: Definition and 905 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. L

    Refraction through different mediums: calculating multiple angles help

    1. I have calculated the first angle using Snell's Law and with subsequent proceeding angles I am uncertain whether my workings are correct since I have used basic laws of geometry that all internal angles of a triangle add up to 180 degrees and that alternate angles are equal to find proceeding...
  2. anemone

    MHB Proving Equality of Angles in an Acute Triangle

    Given that $ABC$ is an acute triangle with $AC>AB$ and $D$ and $E$ be points on side $BC$ such that $BD=CE$ and $D$ lies between $B$ and $E$. Suppose there exists a point $P$ inside the triangle $ABC$ such that $PD$ is parallel to $AE$ and $\angle BAP=\angle CAE$. Prove that $\angle ABP=\angle...
  3. M

    Mechanical Energy of two Cannonballs fired at two different angles

    I solved for both heights: h1 = (1.85x10^4)m, h2 = (5.10 x 10^4)m Question is knowing ME = PE + KE for ball at h1 (angled 37 degrees), is it safe to assume there would be no KE as velocity would equal zero at the highest point? So the mechanical energy = mgh ? Would it be the same for ball at h2?
  4. T

    A Algebraic proof that Euler angles define a proper rotation matrix

    I have asked this question twice and each time, while the answers are OK, I am left dissatisfied. However, now I can state my question properly (due to the last few responses). Go to this page and scroll down to the matrix for sixth row of the proper Euler angles...
  5. alexm

    Motion of rotating rig, find the angle variation with control rod length

    Summary:: We have a rotating arm, offset from the centre of rotation by a certain length, which is controlled by varying the length of a control rod. Need the angle of the rotating arm in terms of length of the rod. The blue line is a fixed column structure. CE and BD form the rotational...
  6. M

    Optical Laser to refract/reflect water vapor and smoke.... angles?

    Building visibiity sensor... What is best angle to detect water vapor reflection from laser, and refraction? I plan to have two open cylindrical containers painted flat black and put inside each other so the overlap is about 0.5-1" (adj to limit ambient light vs airflow). Laser is cheap red...
  7. nomadreid

    Angles of certain complex numbers

    reducing it to various forms: for example, the one in the title, or 2*pi*k(ln m) = a(ln(n/m)), and so forth. My gut feeling is that it is true (that no such foursome exists), but manipulations have not got me anywhere. Anyone push me in the right direction? I am probably overlooking something...
  8. bryanso

    Associated Legendre Function with Angles

    In Wikipedia https://en.m.wikipedia.org/wiki/Associated_Legendre_polynomials, Section Reparameterization in terms of angles, I see this argument: Let ## x = cos\,\theta ## ## \sqrt{1 - x^2} = sin\,\theta ## This is also in Griffiths' Introduction to Quantum Mechanics. Why is this a valid...
  9. B

    How to determine the angles using geometry (specific example)

    I'm trying to find angles α and β. No additional information except: d, h, a. I already tried to figure it out by using isosceles triangles, but this is only true when there is a equilibrium of forces. I thought there are similar triangles incorporated, but I get too many unknown variables...
  10. jisbon

    Finding Angles in a Double slit experiment

    Hello all! Having some problems understanding this question. From what I know, bright fringes means that there will be constructive interferences, whereby ##d\sin \theta =m\lambda## In this case, I know the d (separation of silts). However, what should I put in for wavelength? I went through...
  11. I

    Understanding Tension in Angles: Expert Insights and Tips

  12. Saptarshi Sarkar

    Proving Acute Angles from Two Equations

    From the above two equations, I get : ##2mv = 2mv_aCos(a) + mv_bCos(b)## ##0 = 2mv_aSin(a) - mv_bSin(b)## But, I can't figure out how to prove how the angles should be. I think both the angles should be acute, but don't know how to show it.
  13. Justice Hunter

    Optical What is the Relationship between Angles and....pixels?

    Wasn't really sure how to ask this question since it's kind of niche. I have 3 cameras, which have the property that they occupy no physical space, and have no lens. They are defined only by the angle of their view. Now these cameras capture a certain field and take an image. The cameras will...
  14. K

    Why are these two angles equal (x=z)?,

  15. Z

    Difference between gyroscope angular displacement and Euler angles

    Hi guys, I'm trying to understand between gyroscope angular displacement and euler angles? for example { Δx = Δx + h * Rx * SCx);} this is gyroscope output about anguler displacement.This value can be used to determine angle that device created.Why we should euler angles to fly.(I know...
  16. H

    I Any direct measure of Universe expansion via galaxy subtended angles?

    As indicated in the title and summary, I'm wondering if there is any large scale astronomical effort to assess directly the universal spatial expansion assumed by the Doppler interpretation of the redshift/distance relationship, by measuring individual galaxy subtended angles over time. The...
  17. P

    How can I rotate Euler angles through a specific angle?

    Summary: I found an old topic on this forum that describes a similar problem to what I am facing currently. I want to rotate an object with euler angle values, but the rotation has to be translated based around a specific angle. However, I do not fully understand the solution provided in that...
  18. G

    MHB Solve for the angles in a triangle

    Hi, Could someone check that I'm right with this one, or put me right! I've worked the value out as x=30 and y (2x) = 60. I've come to this as I think it's an isosceles triangle so the base angles would be equal. Am I right? Thank you!
  19. G

    MHB How do I find the angles in a triangle?

    Hi, I'm trying to work out how I'd calculate the values in the below. Rather than just have the answer, I'd really like to understand how I'd calculate this. Thank you in advance!
  20. Avatrin

    A Book to understand Euler angles (and Tait–Bryan )

    Hi I am trying to understand Euler angles and why they work. What are some great books to use as a resource to build a deeper understanding of them? I want to know why 3-2-1 Euler angles are so commonly used, and proofs regarding the mathematical properties of this method..
  21. C

    Finding angles of a Parallelogram

    Hi, I work as a math/science tutor, and a student had this question. He said you're supposed to find the values of x, y, and z and the only information given is that it is a parallelogram. It looks like it might be under-determined to me, every equation I write for it ends up reducing to 15x...
  22. E

    Vectors & Angles Problem Analysis

    Hello, it is my first post here and I am not really sure whether this is the right section. I did not have the chance to take a look at the rules of the forum but I will as soon as I can (I feel a bit guilty for that, I'm sorry...). This is not "homework", I am just studying the amazing L&L...
  23. DuckAmuck

    I Random Unit Vector Angle Difference

    I am simulating random angles from 0 to 2π with a uniform distribution. However, if I take the differences between random angles, I get a non-uniform (monotonically decreasing) distribution of angles. In math speek: Ai = uniform(0,2π) dA = Ai - Aj dA is not uniform. Here is a rough image of...
  24. Eucliwood

    B Measuring Angles: Negatives & Quadrants

    <Moderator's note: Moved from the welcome forum. General question on the measurement of angles and thus no homework.> So we have a physics lab and here's the diagram. I do know how to calculate all but i got negative angle. Does that mean that that angle is reference to the negative x quadrant...
  25. G

    Calculating angles of rotation for 2 interconnected levers

    Hi all, This isn't really "homework" - it's a personal project I'm working on. I'm attempting to animate some mechanical controls of a turbine engine in Adobe After Effects. Having a hard time with the math for "rotating two interconnected points". Here is a photo for visual aid: It's...
  26. A

    Mixed intrinsic and extrinsic angles in 3D rotations

    Being scratching my head for 2 days and not getting anywhere with this one. I am trying to figure out how to perform a 3D rotation described via a mix of intrinsic and extrinsic angles. Here is the problem: I have a platform in the shape of a box with sides of length lx, ly and lz. The platform...
  27. Y

    MHB Sum of the measures of the interior angles of a heptagon

    PLEASE HELP1.What is the sum of the measures of the interior angles of a heptagon? A. 1260∘ B. 2520∘ C. 900∘ D. 1800∘ my answer is C 5.If the sum of the interior angle measures of a polygon is 3600∘, how many sides does the polygon have? A. 22 sides B. 20 sides C. 18 sides D. 10 sides MY...
  28. QuasarBoy543298

    I Understanding 3D Coordinate Rotations with Euler Angles

    I'm trying to wrap my head around the concept. we use 3 rotations to transfer our regular cartesian coordinates (3 x,y,z unit vectors) to other 3 unit vectors. each rotation is associated with an angle. so far I'm good. but now I saw in Landau's and Lifshitz's "mechanics" book this thing...
  29. S

    I Formal proof for the theorem of corresponding angles

    Recently I started looking back at some basic mathematical principles, and I started thinking about the theorem of corresponding angles. It's such a basic idea that it seems obvious on an intuitive level, but despite that (or possibly because of that) I can't think of a good way to formally...
  30. R

    Prove the sums of the angles of any given triangle = 180°

    Homework Statement Prove that if A,B,C, are the angles of an arbitrary triangle, then m(A)+m(B)+m(C) = 180 degrees by the following method: From any vertex draw the perpendicular to the line of the opposite side. Then use the result already known for right triangles Homework EquationsThe...
  31. B

    MHB Left or Right Angles ( + or - ) of adjoining vectors

    Hi there, I have another one for you (Blush) How can I efficiently determine if the angle between 2 vectors is positive or negative... Take a look at this example drawing: Known are the xy coordinates of 2 adjoining vectors, (I also have calcullated the 360 deg angle relative to the x-axis...
  32. T

    A How do I KNOW that Euler angles are sufficient?

    Hello Before I "phrase" my question (and that may be my problem), may I first state what I do know. I understand that a Rotation matrix (a member of SO(3)) has nine elements. I also understand that orthogonality imposes constraints, leaving only three free parameters (a sub-manifold) I also...
  33. I

    Geometrical Optics - Light ray angles on a spherical mirror

    I can't see how the textbook produces the following relationships between angles: $$ \theta = \phi + \alpha \qquad (1)$$ $$ 2\theta = \alpha + \alpha ' \qquad (2)$$ My thinking is that the exterior angle theorem for triangles was used to create expression ##(1)##, but I am unsure as to how...
  34. K

    MHB Find length based on angles

    Hello, What is the value of x in the attached? obviously angle EAD = EDA but then what? the shape is irregular.
  35. K

    MHB What is the minimum value for x in this triangle with angle bisectors AD and BD?

    Hello, In the attached, what is the minimum integer value x can take? AD and BD are angle bisectors the answer is 16 - but i do not know how they did it I am totally stuck, could not think of anything here. The angle bisector formula I know does not fit here
  36. R

    I How do you draw a spacetime diagram and what equation describes it?

    According to Minkowski, spacetime for non-accelerated systems is a four dimensional continuum which has four axes (three space, one time) set mutually at right angles to each other. The velocity of a body moving in a straight line will be the resultant of the component velocities along the...
  37. K

    Trig problem involving a triangle's angles and sides

    Homework Statement In the triangle ABC, angle A = 30 deg, angle B = 45 deg and since AC = a. The perpendicular from C on AB cuts AB in E. In this task you should calculate exact values. a) Determine AE, BC and AB expressed by a. b) Perpendicular from B on AC intersects the extension of AC in...
  38. S

    MHB Angles in congruence triangles

    I am trying to work out the above problem. Known are: D,A,B,a,c,d. I need to work out b,d,G and F. Any ideas? c+d = 90 degrees. Regards, Stan
  39. S

    Projectile motion: Two objects are kicked upward at different angles....

    Homework Statement Two objects are kicked upward at different angles. Object A travels a greater horizontal distance than object B. Both reach the same maximum height. Which of the following statements about the objects are true? You may select more than one. 1.Object A is in the air for a...
  40. H

    MHB Understanding the Relationship between Angles & Diagonals in a Polygon

    There a relationships between angles to diagonals in a polygon?
  41. E

    MHB Law of Cosines: Solve for angles given the sides of triangle

    I've attached the problem and my work. When I enter cos^1(6.890625) I get an error, but 6.9 is also not the answer and Does Not Exist is also not an acceptable answer. So where I am going wrong with this?
  42. alexi_b

    River question (looking for angles and headings)

    Homework Statement A child in danger of drowning in a river is being carried downstream by a current that has a speed of 2.35km/h. The child is 0.505km from shore and 0.780km upstream of a boat landing when a rescue boat sets out. If the boat proceeds at its maximum speed of 18.8km/h relative...
  43. KristinaMr

    Angle between radius and acceleration

    Homework Statement A particle is moving clockwise in a circle of radius 2.50m at a given instant of time. I have to find radiant and tangential acceleration and the speed of the particle. The acceleration vector is 15.0 m/s² and the angle between the radius and the acceleration vector is 30°...
  44. Jan Berkhout

    How do I do this trigonometry vector calculation?

    Homework Statement A pilot wishes to fly at maximum speed due north. The plane can fly at 100km/h in still air. A 30km/h wind blows from the south-east. Calculate: a) The direction the plane must head to fly north. b) Its speed relative to the ground. Homework Equations Sine Rule...
  45. B92X

    List of drag coefficient for basic shapes has no angles

    When I type "drag coefficient" in Google, and view some of the images, the standard list of geometrical shapes come into view, such as this one: https://upload.wikimedia.org/wikipedia/commons/thumb/3/37/14ilf1l.svg/220px-14ilf1l.svg.png If we take the cone for example, there is a drag...
  46. G

    Angles inscribed in circles part 1

    Homework Statement OK, I am new to these kinds of problems and I am trying to learn the appropriate properties but they are proving somewhat difficult for me... I hope I am going in the right direction. Homework Equations [/B] The first problem corresponds to the figure with 'Rep' in the...
  47. J

    MHB Find Rhombus Angles: 360º & 22º30

    The angle between the diagonal and the side of the rhombus is 22º30’. Find rhombus angles. Rhombus interior angles are 360º that much I know, but how do I find out the other angles?
  48. Cocoleia

    Particle decay, Lorentz transformations with angles

    Homework Statement I have a mother particle at rest, which decays to a daughter particle. The daughter has mass m, momentum p and energy E and is at an angle θ1. Now I have to assume that the daughter is emitted at an angle θ2, and the mother is moving along the x-axis with velocity βc. I need...
  49. C

    MHB Secant and Tangent Angles in Circles, finding an arc length.

    I got 138.17, but that isn't correct. I don't know how to do it, since the only way I thought, gave me the wrong answer. Can anyone help?
  50. B

    Why are the angles in rope equilibrium the same?

    Homework Statement Between two parallel walls we tighten a rope. One end of a rope is tied a little higher on the wall than the end on the opposite wall. On the rope we put a pulley with mass m which slides to equilibrium position. Homework EquationsThe Attempt at a Solution I assumed that in...
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