What is Angles: Definition and 908 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. E

    Find two angles where the directional derivative is 1 at p0

    1. Given a function f(x,y) at (x0,y0). Find the two angles the directional derivative makes with the x-axis, where the directional derivative is 1. The angles lie in (-pi,pi]. 2. f(x,y) = sec(pi/14)*sqrt(x^2 + y^2) p0 = (6,6) 3. I use the relation D_u = grad(f) * u, where u is the...
  2. A

    What is the notation for angular distance travelled?

    What is the notation for the angular distance traveled by an object moving in circular motion? s is for regular distance (m,ft,inches, etc.). What I want is some x to be the distance in either degrees or radians. How should I call that x?
  3. K

    Organic chemistry hybridization and bond angles

    Homework Statement Determine the hybridization of the atoms labeled A, B and C in the molecule and the bond angles around them. Homework Equations N/A 3. The Attempt at a Solution A. Normally, I would say it is sp3 for oxygen since there are 4 groups attached to it including the lone...
  4. X

    Compound Angles: Find Exact Value of cos(a+b)

    Homework Statement Angle a is located in the second quadrant where sin a=2/5 and angle b is located in the third quadrant where tan b=3/4. Determine an exact value for cos(a+b) and where it is located. Homework Equations cos(a+b)=cosacosb+sinasinb The Attempt at a Solution I don't know what...
  5. E

    Floating in space and angles of galaxies

    With the way our universe looks, different galaxies are angled in various ways from our perspective. What is the cause of this? My initial thoughts would be based on how spacetime is curved, or maybe it's because of the angle of rotation of the black hole at the center of those galaxies...
  6. A

    MHB Given 3 sides of a triangle, compute interior angles and area

    Just attempted another exam question. Would you mind correcting me if I am wrong? The question is A triangle ABC has sides of length AB= 3.5 m, BC = 5.1 m and AC = 4.2m. a) Calculate the size of the angle B and the size of the angle C, in degrees correct to 1 decimal place, in each case...
  7. D

    What's the best device for measuring angles?

    << Moderator Note -- Dorea is an instructor asking about their physics lab >> The first experiment in our fundamental physics lab is "Measuring & Measurement errors". Currently we have four devices: - rule (0.5 mm) - Vernier Caliper (0.02 mm) - Micrometer (0.01 mm) - Spherometer We're seeking...
  8. A

    The sum of angles in 3D is not 90 while in 2D it is?

    Sorry for the confusing tittle but I could not explain it better. Here is what I am trying to ask: When you have 2 axis(x and y) such as the image below, the sum of the two angles, a and b will always be equal to 90 degrees. a + b = 90degrees However when you add a 3rd axis(x, y and z, making...
  9. ltkach2015

    Alternative Vector Method to Finding Angles of Vertices of Triangle?

    NOTE: I know the solution, but I challenge it. Specifically, I feel that the generally accepted solution to this problem is not intuitive. I have shown the accepted solution, and below that I have shown what I feel seems more intuitive (from a geometric standpoint)...
  10. A

    Transforming Spherical Angles to Cartesian Coordinates for Beam Dynamics

    Hello I have this problem - From a generator, I get a compton scattering with the electrons theta and phi angles. where I having the following equations for a particle px = E_particle * sin (theta) * cos (phi); py = E_particle * sin (theta) * sin (phi); pz = E_particle * cos (theta)...
  11. Mr Davis 97

    Force components of two strings tied to a painting at 45 degree angles

    Homework Statement Find the equation of the horizontal components of two strings tied to a painting at 45 degree angles with the horizontal.Homework Equations Fnet = 0The Attempt at a Solution Since the painting is in equilibrium, I found that, in the horizontal direction, Fnet = 0 = S1x -...
  12. D

    How do angles of waterwheel affect angular velocity

    Hello, I'm currently writing a high school academic paper on waterwheels. One of the things I want to find out is whether the angle of paddles of the undershot waterwheel affects the angular velocity. So here is my question: How do the different angles of the paddles in a waterwheel affect...
  13. S

    2D Elastic collision of varying mass, velocities, and angles

    Problem statement: Two pucks of radius 0.05 meters collide as shown in attached picture. The mass of puck 1 is 0.1 kg and that of puck 2 is 0.15 kg. The initial velocities are v1i = 1 m/s and v2i= 0.6 m/s. (1) Assuming no friction between the pucks, only normal forces during collision, in...
  14. T

    Friction Force Calculation at an Angle on Flat Surface

    how do you find friction force when applied force is at an angle, this is on a flat horizontal surface.
  15. C

    Hockey Rink Optimization problem

    Homework Statement [/B] Solve optimization problem; A person is to skate up a hockey rink, in a straight line(parallel to both of the sides), from wherever they are standing. They are to shoot the puck into the net whenever they reach the point where the angle on the net is the largest. Need to...
  16. P

    Bond Angles, Bond Lengths and Hybridization

    Consider the hypothetical molecule 1,3,5-cyclohexatriene (not benzene, I am referring to a molecule where no resonance takes place - a molecule with three C=C bonds and 3 C-C bonds). Each carbon atom in this molecule would be participating in one double bond, and so each carbon atom would be sp2...
  17. P

    How Do You Calculate the Maximum Angle of Inclination After a Collision?

    Mentor's note: this was originally posted in a non-homework forum, so it doesn't have the homework template. ------------------------------------Hey guys hoping you guys could help me with this A object (20g) moving horizontally at 100m/s embeds itself in the middle of a block of some wood...
  18. M

    Find Max Mass B for Mass A to Move on Slope of 30°

    Homework Statement A mass(A) of 12kg is on a slope with an angle of 30 degrees. The static coefficient of friction of the slope = 0.5 (μs) The kinetic coefficient of friction 0.3 The length of the slope from the block= 5m However the The mass(A) is connected to another mass(B) which is...
  19. M

    Light angles measured in a moving reference frame

    I've managed to get through all of this question without trouble until part d). The full question is given here: I've calculated the "true" angles of Star A and Star B as 71.57 degrees and 45 degrees respectively in Frame S, and the "light" angles should be the same, since the stars are...
  20. S

    Calculating Required Heading for North-East Sailing with Current at 5km/h

    Homework Statement A ships captain wishes to sail his ship north -east. A current is moving his ship with a velocity of 5.0km/h . If the ship has a maximum speed of 30 km/h what is the ships required heading? Homework Equations Cos angle=A/H The Attempt at a Solution Heading=cosine (5/30)...
  21. Femme_physics

    Average/typical twist angles of a jet turbine blade

    Hi guys, I'm trying to find info with respect to twist angles of a turbine blade (for airplane engines, let's say)... I read somewhere on the forum that it's typically 0-20 degrees. I'm trying to look for quoted sources though or at least second opinions on that matter.
  22. P

    Why does Methane lack 90 degree angles?

    With the Methane structure of CH4 and an electron structure of Carbon as 1s22s22px12py1 and the electron structure of Hydrogen as 1s1 with P-orbitals separated by 90 degrees from each other and S-orbitals uniform spheres why aren't two of the Hydrogen atoms in a Methane molecule at 90 degree...
  23. C

    Need help with a problem (sum of two angles)

    Homework Statement Hello, all. This here's the problem: Use the difference formula to solve for the exact value of tan(15°). Homework EquationsThe Attempt at a Solution I've solved it up until this point: I used the formula to get (tan(45°)-tan(30°)) / (1 + tan(45°)tan(30°)). (1 -...
  24. B

    Regarding vectors, resultants, and angles

    I have two problems that I cannot seem to figure out. I already know the answers, but I want to know the process of how to complete them so I know for quizzes and tests. 1. Vector A is 3 units in length and points along the positive x-axis; vector B is 4 units in length and points along a...
  25. G

    Finding Min Value of Sum of Cosine Angles in 3D Space

    Dear Friends! How can I find the minimum value of sum of cosine of angles between three unit vectors in three dimension space
  26. xatu

    Why are these angles the same?

    Homework Statement In my statics book (13th ed. Hibbeler) I'm reviewing the section about using vector analysis to calculate the moment of a force about a specific axis. I understand the theory fine, but I don't completely understand the figure in the book (pic attached). Specifically, why are...
  27. F

    Issue with angles in torque problem?

    Ok so for this example you have to calculate the net torque about an axis that passes through the hinges in each of the following cases in the image: a) and c) were fairly straightforward to calculate but i had issues with b) and c). The solution listed the angle for b) as sin(115°) and for...
  28. Bassa

    Vector product and vector product angles

    Hello! I have a problem in my calculus based physics class regarding vectors. The problem says: Vectors A and B have a scalar product -6.00 and their vector product has magnitude 9.00 what is the angle between these two vectors? Here is how I approached it: -6=|A||B|cos (theta) 9=|A||B|sin...
  29. C

    Basic trig question: reference angles

    Hello, Preparing for a test, I've had to go through some very basic trigonometry and I've got to thinking why reference angles "work". I've gone through my study material and through another trigonometry book I have around the house and references angles are never proven, the theorem is just...
  30. X

    Phasor Leading and Lagging Angles

    Consider two voltage phasors: V1 = 1 volt @ 50°, and V2 = 1 volt @ 30°. It follows then that the relative phase shift between these two phasors can be expressed by any of the four following descriptions in terms of leading and lagging angle relationships. 1.) V1 Leads V2 by 20° 2.)...
  31. Feodalherren

    Solving for F1 Angle Components using Spherical Coordinates

    Homework Statement Specify the coordinate direction angle α,β,γ of F1. Homework Equations The Attempt at a Solution γ= 90-30 = 60 The only obvious one. I have no clue how I'm supposed to see what the other are. α seems to me like it's 320 degrees because if you rotate in the...
  32. B

    MHB Trigonometric function values of quadrantal angles

    I can't seem to solve 7 cot 270° + 4 csc 90° I don't know whether I'm entering something in my calculator wrong (could've sworn I was doing it right earlier) or if there just isn't an answer. In my calculator, I enter 7/tan(270°)+4/sin(90°) and it gives me a domain error.
  33. J

    Photon entanglement: why three angles?

    When the two polarizers are set 60 degrees apart, for example, QM prediction is 25% correlation. It is already different than what is believed to be classical or "expected" result. So what is the point of testing more than one angle in a single experiment? And what difference does it make when...
  34. 2

    Why is a pendulum only simple harmonic motion for small angles?

    Homework Statement Hi all! I'm slightly confused about pendulums and simple harmonic motion. In my textbook, it says that a pendulum only exhibits simple harmonic motion when the angle is small (<10 degrees). I was wondering why this is, using equations if possible. Without the math, I think...
  35. Govind_Balaji

    Proving ∠D=90°-(∠A/2) in Triangle ABC with Bisectors

    Homework Statement ABC is a triangle. The bisector of the exterior angle at B and the bisector of ∠C intersect each other at D. Then prove that ∠D=90°-(∠A/2) Homework Equations The Attempt at a Solution I guess I want to prove an untrue thing because by drawing a diagram and...
  36. S

    How Does Light Refract Through a Prism with Different Angles?

    Homework Statement Light is incident on a glass prism with an angle of incidence of 54°. The light enters on the left hand side of a triangular prism with base angles of 80° and apex angle of 20°. (The 54° ray of incidence enters from the south west side of the prism, directed towards the...
  37. D

    MHB Equality of Angles: 3 Equal Angles in a Picture

    Can you explain why the 3 angles in the picture are the same.
  38. C

    MHB How do I find missing angles in trigonometry and geometry?

    Someone please take a look at the attachment above. These two questions have me stumped and it ask on each question to find three missing angles. I don't even know where to start. Could someone be so kind and explain to me how to figure each of these. I need help with this asap to help my...
  39. A

    MHB What is the rate of change of angle in a 90 degree triangle?

    Hey guys, I need some more help for this problem set I've been working on. I'm doubting some of my answers and I'd appreciate some help. This is only for question 1. Ignore 2. Question: For the first one, drawing out the question clearly tells us that we are working with a 90 degree...
  40. HeavyMetal

    The Difference in Refraction Angles of Different Colored Light

    As I understand it, when you beam white light through a glass prism, light disperses and refracts. Red light refracts the least and violet light refracts the most. I am dying to know: why do different frequencies of light have different angles of refraction? Specifically, why is it that an...
  41. S

    Can You Find All Triangle Angles from 2 Sides?

    Homework Statement Is it possible to determine all the angles in a triangle, if we only know the length of two sides?Homework Equations The Attempt at a Solution I was thinking for quite some time and I don't think it is possible. It probably is, if two sides are peprendicular but if not, I...
  42. T

    MHB Calculation of angles in normal anatomical curved bones that are fractured.

    Hi, I am an orthopedic surgeon. Many of our long bones are anatomically curved. When they fracture they sometimes heal in a none perfect/anatomic position. How do one calculate the angle/curve or changed angle/curve of a fractured bone healed or fixed none anatomically Please see my drawn...
  43. D

    MHB Solve Trigonometry Angles: Degrees, Minutes & Seconds

    please help me to solve these problems, 1. how many degrees, minutes, and seconds are respectively passed over in $11\frac{1}{9}$ minutes by the hour and minute hands of a watch? 2. The number of degrees in one acute angle of a right-angled triangle is equal to the number of grades in the...
  44. S

    Possible complex angles with no imaginary periodicity

    Trying the already known equation, sin^2(x) + cos^2(x) = 1 i wondered what would happen if i took that either sin(x) or cos(x) squared equalled a number greater than 1, so when i plugged in sin(x) as 5/3 i got cos(x) 4i/3 , went to euler's equation and added the results, then put the...
  45. anemone

    MHB Solve the triangle PQR by finding their angles

    $QB$ and $RA$ are angle bisectors of the triangle $PQR$. Given that $\angle QBA=24^{\circ}$ and $\angle RAD=18^{\circ}$. Find the measure of each angles $P,\,Q$ and $R$.
  46. T

    Help with Finding Angles of an Octagon

    Hi all I was wondering if someone could help with the following:- I have a regular octagon. Find angle CBA, ACB, BAC. Lines BA and AC are equal in length. I have done the following:- Found all the internal angles and all the external angles. I know that I have an...
  47. P

    Can We Define Angles in Flat Spacetime Using Geodesics?

    In another thread, it was asked if we could use the angular deficit idea to determine curvature not in space, but in space-time. My idea to attempt to proceed along these lines would be to generalize the idea of angle, but I don't have anything that I feel I can point to. As a starting...
  48. T

    Diagonalization of 8x8 matrix with Euler angles

    I am trying to diagonalize the following matrix: M = \left( \begin{array}{cccc} 0 & 0 & 0 & a \\ 0 & 0 & -a & 0 \\ 0 & -a & 0 & -A \\ a & 0 & -A & 0 \end{array} \right) a and A are themselves 2x2 symmetric matrices: a = \left( \begin{array}{cc} a_{11} & a_{12}\\ a_{12} & a_{22}...
  49. anemone

    MHB Prove one of the angles of triangle is 60°

    Given that $PA,\,QB,\,RC$ are the altitudes of the acute triangle $PQR$ such that $9\vec{PA}+4\vec{QB}+7\vec{RC}=0$. Show that one of the angles of triangle $PQR$ is $60^{\circ}$.
  50. Q

    Tetrahedron; Sum of Bond Angles

    Homework Statement Prove that if bonding-pair repulsions were maximized in CH3X, then the sum of the bond angles would be 450°. Homework Equations In a perfect tetrahedral molecule (e.g. methane), the sum of the bond angles is about 438 degrees (109.5° times 4). The Attempt at a...
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