What is Angle: Definition and 1000 Discussions

In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes. These are called dihedral angles. Two intersecting curves define also an angle, which is the angle of the tangents at the intersection point. For example, the spherical angle formed by two great circles on a sphere equals the dihedral angle between the planes containing the great circles.
Angle is also used to designate the measure of an angle or of a rotation. This measure is the ratio of the length of a circular arc to its radius. In the case of a geometric angle, the arc is centered at the vertex and delimited by the sides. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation.

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  1. T

    Another angle of "Why do you need a line 2 on a circuit?"

    I know that on an alternating current circuit, you have to have both a line 1 and a line 2 to have a circuit. Here is a pictorial diagram of an alternating current circuit: In a previous thread, I asked why would an AC circuit like in Diagram 2 not work? Here is a photograph of diagram 2...
  2. M

    Fluids: Kistler contact angle model

    Hi PF! I keep seeing Kistler's contact angle model wrote like this $$ \theta_d = f(Ca+f^{-1}(\theta_e)) : f = \arccos\left( 1-2\tanh\left( 5.15 \left( \frac{x}{1+1.31x^{0.99}} \right)^{0.706} \right) \right) $$, where the plot then has a sort of break, something like this: But this is not the...
  3. xyz_1965

    MHB What is the formula for finding angle theta without accounting for height?

    Here is my set up. Let t = theta for short tan(t) = 324/550 arctan(tan t) = arctan(324/550) t = arctan(324/550) Correct thus far? Note: What does "not to scale" mean in other words?
  4. xyz_1965

    MHB What is the Angle Formed by a Leaning Ladder Against a House?

    A 16 foot ladder is leaning against a house. It touches the bottom of a window that is 12, feet 6 inches above the ground. What is the measure of the angle that the ladder forms with the ground? I will use sin (x), where x is the measure of the angle that the ladder forms with the ground. I...
  5. tanaygupta2000

    Angle of deviation from a magnetic field

    The beam of protons are directed towards the axis of the cylinder, perpendicular to the direction of the field. While traveling through the cross-section of the cylinder, the proton beam experiences a magnetic force, which tends to move the beam in a circular orbit of the radius given by: r =...
  6. T

    A different angle of Why do you need a line 2 on an AC circuit?

    Preface to thread: I am darn well aware of the fact that on an AC circuit, there has to be a line 2 after the load to bring current back to the power source. This thread is about WHY does there have to be a line 2 after the load to bring current back to the power source. I hope that I don't...
  7. Kayla Martin

    How to calculate a solid angle in steradians from arcminutes?

    I tried $$\Omega = \pi(\frac{\theta}{2})^{\frac{1}{2}}$$
  8. Leo Liu

    Is the length of the arm r in a polar coordinate a function of the angle?

    My textbook says ##\vec r (\theta) = r \hat r (\theta)##, where ##\hat r (\theta)## is the terminal arm (a position vector in some sense). It can be seen that both ##\vec r (\theta)## and ##\hat r (\theta) ## are function of ##\theta##; whereas, the length of the vector ##r## is not. I...
  9. wrobel

    Two cylinders rotating with contact at an angle (reformulation of the problem)

    Some time ago there was a problem with the following picture somewhere out here. I think this problem was underestimated a little bit. Let us reformulate the problem. Assume that each cylinder, if it was not influenced by the other one, could rotate freely about its fixed axis. But the...
  10. E

    Surface tension and Young's contact angle

    I came across this diagram, the ##\gamma##'s are supposedly forces per unit length of the respective interfaces: It's not clear what these forces are acting on. ##\gamma_{SL}## and ##\gamma_{LG}## look like they could be acting on a small bit of water right at the end, but I have no idea what...
  11. P

    Rotation of two cylinders inclined at an angle

    A single pair of points will be in contact between P and Q. The frictional force will try to make the velocity of these points equal. Say the final angular velocity of Q is ωq. The velocity of points in contact can never be equal because of difference in directions of ωq and ωp. If I break...
  12. B

    Engineering Angle of twist and Shear stress in a shaft

    Hello, I have attempted the question below. I think i have correctly completed the question. Could anyone see if i have gone wrong? As trying to learn this. I am just worried about the units m to mm. Also the answer being correct, 917.6Gpa. I was unsure what units to use on the answer...
  13. Z

    Find the angle required for a 3kg block to slide down an incline

    This is a rough sketch of the model. It is frictionless. I originally tried simple right-angle trig (sin θ =opp/hyp), but that just ends up as sin θ = sin θ , as well as cos θ = cos θ. I feel like there's also a way to manipulate dynamic equations around to equate something that is capable...
  14. S

    I Find Angles in Right Angle Triangles

    If it we know 3 sides of a right angle triangle, will it be possible to calculate the angles without using trig. Functions
  15. A

    How to determine the effect of counterforce on the angle of force

    Can anyone help me with a formula that would show the effect the counterforce of the neck will have on the direction the knife is moving, to be able to determine what a cut in a given direction what will be its direction of force? (I apologize for not following the guidelines for homework...
  16. DerbisEternal

    How do I proceed with two different trig functions containing x on the left?

    Given the total angles in the x direction, I set up this: (mg/cos(x))*sin(x)-Fe=0 then isolated for x: mgtan(x)=(kq^2)/(2*sin^2x) sin^2(x)*tan(x)=(kq^2)/(2mg) From here I am stuck. How do I go forward when x is contained in two different trig functions on the left?
  17. WMDhamnekar

    MHB How to find angle between two vectors, given their spherical co-ordinates?

    I know that $\arccos{(\cos{\phi_1}\cos{\phi_2}+\sin{\phi_1}\sin{\phi_2}\cos{(\theta_2-\theta_1)})}=\gamma$ But how can i answer the above question? If any member knows the proof of this formula may reply to this question with correct proof.
  18. C

    MHB Find the Bearing from A to C & Angle B: Solve Here

    Dear everyone, An airplane flies 470 miles from point $A$ to point $B$ with a bearing of 25 degrees. It then flies from 250 miles from point $B$ to point $C$ with a bearing of 40 degrees. Find the distance and the bearing from A to point C. Work I understand that I need to use law of...
  19. PainterGuy

    Brewster's angle and the intensity of reflected light

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  20. dykuma

    How Can I Accurately Determine the Critical Angle in an Unknown Material?

    First, I attempted to find the wavelength of the incident wave in the required terms: Next, I tried to find the wavelength inside of the material: And then lasted, I tried to find the critical angle: My issue is that 1) I don't know if what I did was correct. 2) I don't think what I did...
  21. Pushies

    CoM reduced by total body height when bending your knee X degrees

    Lets say that a man with a standing height of 185cm bent his knee 30 degrees, how many centimeters will be reduced from his standing height? Assume his femur length is 60cm and his tibia (shin) length is 50cm. Can anyone give me a hint? I've tried to use trigonometry but i don't think i fully...
  22. M

    MHB Acute angle of right triangles

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  23. D

    Not sure if I have the correct angle and mass for this sum of forces

    Balance the forces east-west: 3.5kg*sin45º + 4.2kg*cos30º - 4.8kg*sin30º - E*cosΘ = 0 E*cosΘ = 3.712 kg balance north-south: 2.8kg + 3.5kg*cos45º - 4.2kg*sin30º - 4.8kg*cos30º + E*sinΘ = 0 E*sinΘ = 0.982 EsinΘ / EcosΘ = 0.982 / 3.712 tanΘ = 0.2645 Θ = 14.8º ◄ E = 3.712kg / cos14.8º = 3.84...
  24. k2ace

    How Much Weight Can My Angle Bracket Rails Safely Hold?

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  25. marciokoko

    Solve angle issues for opening a door with a linear actuator

    ok, setting the force issues aside (for now), Id like to use what I know about triangles to figure how to position my linear actuator in order to open and close this door correctly: The vertical side is 84cm, the door is 92cm. The measured stroke of the AL is 25cm. I would need to lower the...
  26. Tony Hau

    Potential energy as a function of the square of this angle

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  27. Eclair_de_XII

    B Rotating a point in 3-space through an angle about some vector

    Denote ##v=(1,2,3)^T##, ##\theta=\arctan(2)##, and ##\phi=\arctan(\frac{3}{\sqrt{5}})##.The way that I attempted this was by performing the following steps: (1) Rotate ##v## about the z-axis ##-\theta## degrees, while keeping the z-coordinate constant. (2) Rotate ##v## about the y-axis...
  28. P

    Conical pendulum: what are the tension and the angle?

  29. nuclearfireball_42

    Can I determine the phase angle of this equation by using the sin function?

    I've got the answer for (a). It's k = 0.78 N/m. I'm having problems with (b). I know that the equation of displacement in this case should either be : x(t) = Asin(ωt + φ) or x(t) = Acos(ωt - φ) where A = amplitudeFrom what I understand, both the equation above should give the same result as...
  30. S

    B Angle Potential: Exploring Meaning & Natural Phenomena

    I have been trying to understand angle potentials such as described in this website, https://lammps.sandia.gov/doc/angle_style.html . Supposing two bonds have a certain angle they have to adhere to, what does this mean for that one atom being bound to, that only x amount of atoms can bind with...
  31. 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...
  32. AzureSekki

    Engineering Was the Angle Discovered? Thread Closed Due to Existing Problem

  33. V

    Second reflection angle of incidences in 3D

    Given Theta1(angle of incidence) and alpha1(azimuth angle). how do we obtain the second reflection angle theta3 and alpha3? Assuming the surface to be a mirror reflection(theta1 = theta2). Need an equation when varied the incident angles we would obtain the second reflection angles or a method...
  34. BiggestAfrica

    Determining speed at an angle using an energy balance

    I first found the height of the ball after it's passed the 45 degree angle by doing 4.12*sin(45) = 2.9133, and plugged in the rest of the variables (masses cancel) .5(m)(vo^2) = (.5)(m)(vf^2) + mgh (17.5^2)(.5) = (.5)(vf^2)(9.8*2.9133) vf = 15.7845, however this is incorrect I don't understand...
  35. N

    I Selective filter based on angle of incidence?

    I am a using a mirror to reflect an image at an angle of incidence of 10 degrees. The mirror is also at an angle of incidence of approximately 30 degrees from the viewer and it creates undesired reflections when looking at the mirror. Here is a diagram illustrating the situation. I am looking...
  36. K

    The Determination of the Launch Angle of a Projectile

    Hi, I am new here to the forum and I am having trouble with a project that I am undertaking with some friends. We are trying to build a firefighting robot. I am trying to derive an expression to solve for the launch angle theta of the water so that at x (meters), the projectile will be at 0.33...
  37. L

    Initial velocity given time and angle

    From Ball 1 I can can determine it's initial velocity and then maximum height. I'm not sure how this is relevant, as I cannot find a formula using angle, time, height and velocity. I have found h=V(squared) x sin (squared) Theta / 2g and also t=2Vsin Theta/g. These give similar, but different...
  38. C

    I Why the reflected angle is the same as incident in x-ray diffraction?

    I'm reading about x-ray diffraction in the context of crystal structure determination. Usually this discussion begins with Bragg's law, $$2d\sin\theta=n\lambda,$$ where ##\theta## is the angle of incoming and "reflected" x-rays. This is the bit that bothers me. I understand that the...
  39. B

    At what angle do we have to kick a ball up the hill for n-rebounds?

    I decided to try and find a solution in a green (tilted) coordinate system. I started solving this problem with thinking about 1-rebound: ##⟹y=0, α=\text{angle under which we kick a ball}##; ##y=sin\alpha v_0t-\frac{1}{2}gt^2##; because I'm trying to solve this in a tilted system, I have to...
  40. J

    MHB Amplitude, Period, frequency and phase angle

    HELP! totally lost and confused with this question: A machine is subject to two vibrations at the same time. one vibration has the form: 2cosωt and the other vibration has the form: 3 cos(ωt+0.785). (0.785 is actually expressed as pi/4) determine the resulting vibration and express it in the...
  41. neilparker62

    I How Does Elastic Collision Angle Relate to Mass Ratios?

    Large mass (M) - moving - collides elastically with stationary small mass (m) as per crude diagram below. Angle θ is formed between the initial path of the large mass and the line of centres during collision. I would like to say that maximum deflection of the large mass occurs when cos(θ)=m/M so...
  42. wicker558

    Object thrown at an angle: Initial velocity has to equal speed at t

    My solution is very sketchy, but we want the math right. However, I've came to 2 thoughts that helped me get to the solution, and those are: The only way that you can launch a ball at a velocity and have it be the same velocity two seconds later, is if it's already reached its maximum height...
  43. N

    I Finding the Sun's Angle from Longitude, Latitude & Time/Date

    If you had your longitude/latitude, and the time/date, how could I go about working out the angle between your normal and the sun? At first I was doing a simplistic approach of assuming elliptical orbit in only two dimensions and that the Earth is a perfect sphere,Can I get a more accurate...
  44. B

    Finding the angle between a wall and a broken rope

    I tried to work out the solution using h. I get a trapezium, but there is always a lack of additional information. I looked up the solution and BAM, there is this simple equation for sinα. I really don't understand how do we get such a solution. I leaned you can use trigonometric functions in a...
  45. E

    Inclined Planes, finding time from acceleration at an angle

    Because the friction is the same in both parts, the calculated acceleration from (b) should be the same for (c) I knew I could find Vf, and thought I could do it with an energy equation Ei=Ef mgh=1/2mv^2 gh=1/2v^2 (2)9.81(1.5)=1/2v^2(2) (square root)29.43=(square root)v^2 v= 5.424 Then...
  46. M

    A kid slips off the top of the hill -- find the escape angle

    Hi, This is my try. Are you in agreement with this ? Thanks.
  47. M

    Moving a box on an inclined plane. Find F(min), angle and W(min)

    Hi, this is my try: I would appreciate any confirmation or correction . -- Thanks
  48. A

    Brewster's angle, dipole radiation and refraction

    So I was wondering how it is possible that there will be no p-pol light reflected when the refracted light is at 90 degrees to the reflected light (so incoming light is at Brewster's angle). The Brewster's angle was explained to me by saying that the electrons in the medium radiate light...
  49. Carbretta

    Engineering Calculating Shear and Tensile force in a rivet at an angle

    Hi all! I have used this forum a few times and it has been very helpful, however now I am stuck. I have completed the question above however I have conflicting information regarding the Tensile and Shear force being applied to the rivet. I use the following calculation for this: Shear Force...
  50. Athenian

    [Special Relativity] - Finding Angle θ as Measured in Frame S

    Below is the attempted solution after researching the contents available on Introduction to Electrodynamics by Griffith. To begin with, I defined the rod as having a length of ##l'## at rest in frame ##S'##. Thus, in frame ##S'##, the height of the rod is ##l' sin(\theta ')## and its horizontal...
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