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. N

    Projectile Angle and Distance problem

    Homework Statement A projectile was launched from the top of a 100m tower upward at an angle theta to the horizontal with an initial velocity of 36m/s. The time of flight of the projectile was 8 seconds. Determine: i) The angle of projection ii) The maximum height reached by the projectile...
  2. Q

    Find the tension in the rope pulling a box at an angle

    Homework Statement Homework EquationsThe Attempt at a Solution Here is what i have done so far: Fx = cos 45 T - Ff =ma Fy=sin 45 T -mg+ Fn =ma I found ff= uk * Fn = 0.5 *sin 45 +mg fn = sin 45 +mg Isolated for T in the x and y: Tx = ma + Ff / cos 45 = 13.404 Ty = ma +mg - Fn / sin 45 =...
  3. S

    Maximum angle between resultant and original vector

    Homework Statement Two vectors of magnitude 5 units and 3 units are added such that the angle between the resultant and the vector of magnitude 5units is maximum. Find this angle. Homework EquationsThe Attempt at a Solution Knowing that the resultant vector makes a smaller angle with a...
  4. Designman

    Resultant angle of a suspended body after torque is applied

    A body in an absolute vacuum is suspended from an axle having no friction at the body or at the suspension points. A power source is affixed to the body which rotates the axle. At rest the body is horizontal. The body weighs 4000 lbs. The center of gravity of the body is vertically 4 ft. below...
  5. StarWarsNerd

    Angle of Deflection in Elastic Collision

    This is the problem I am looking to solve: given two objects of different mass, find the angle of deflection after an elastic collision for each object. For both objects we know: m : Mass in Kilograms θi : Initial Angle in Degrees si : Initial Speed in Units per Second sf : Final Speed in...
  6. G

    Strain of a wire tied with an angle in a beam

    Well, i have a cantilever beam where i have the displacement of the tip of the beam (y axis) data from a vibration of this beam. In the tip of the beam is a steel wire attached, pulling up the beam with an angle (30º for example). I want to know if exists a form to obtain the strain of the wire...
  7. B

    Question about Centripetal Force

    Homework Statement Question 2.b. from this paper - http://www.sqa.org.uk/files_ccc/PhysicsEQPAH.pdf Homework Equations let theta = x Tcosx = mg Tsinx = 2.5 (2.5 is the centripetal force) The Attempt at a Solution I rearranged the above equations and got 52 degrees as my answer. The...
  8. S

    Brewster's Angle and P-Polarization in Laser Design

    Homework Statement Fresnel losses occur between two different media that have different refractive indices. To reduce these losses we can change the angle of incidence to brewster's angle. At this angle, the amount of reflective loss is minimized for p-polarized light. Do we assume that laser...
  9. Z

    For which incidence angle the ray won't come out of the prism's surface....

    Homework Statement A ray of light falls on the surface AC of a prism with a straight angle and with two sides equal. For which incidence angle the ray won't come out of the surface AB. The index of refraction for the prism is n=2. Homework Equations sina/sinb=n2/n1 The Attempt at a Solution...
  10. Z

    When the incidence angle is equal to the angle of refraction

    Homework Statement When the incidence angle is equal to the angle of refraction? Homework Equations sina/sinb=n2/n1The Attempt at a Solution I think as a=b => sina=sinb => n1=n2. We should have the same environment? But is that refraction?
  11. T

    I A question on towing through an angle

    Hello friends, I have a situation where I am looking to pull a load and would like to better understand the forces involved. In the first scenario I am pulling a load in a straight line, the load cell reads 10kN. In the second scenario I would like to pull the same load at an angle of 150o...
  12. G

    Finding the Angle of Cut for a Spherical Fruit Slice

    Homework Statement A spherical fruit has a radius of 1 inch. A slice has surface area of its peel equal to pi/8 . Determine the angle of cut for the slice. Homework Equations I'm sure there is a relevant equation here but I don't know it :-( The Attempt at a Solution So the radius is 1 inch...
  13. A

    Thrust angle calculation for off-centerline airplane engine

    This isn't for any particular project or assignment, but I've tried solving this in the past and haven't figured it out. Say you have an RC seaplane, like the one pictured, with the engine mounted well above and aft the CG. You're going to need to angle it down a little to counteract the...
  14. IBNU1

    Find Angle of Refraction: Snell's Law Solution

    Homework Statement I need to find how a ray of light will travel from the snail towards Andrews eye. I need to find the angle of incidence and angle of refraction. I know the index of refraction of both materials Air: 1 Water 1.33 Homework Equations Snells law 1.33 *sin(X) = sin(y) x is...
  15. gracy

    B Angle between two vectors book problem

    Should not angle between vector P and Q be 180-θ rather than θ? According to my book it is θ.
  16. A

    Does coefficient of static friction change with angle

    Hi all, I am very confused by this concept. As I searched online, all respondents say that friction decreases as angle increases because normal force decreases. BUT, they don't explain this phenomenon: A block on a ramp is static at certain angle, and after the ramp is raised by a certain...
  17. A

    Steering angle for Autonomous vehicle

    Dear All, Hello, I'm studying electronics engineering and I'm new in vehicle dynamics, Recently, I make an autonomous vehicle for my final project. In order to control steering angle of vehicle, I have difficulty to measure the steering angle based on curvature road and vehicle velocity. Anybody...
  18. Z

    Angle of incidence and refraction

    Hello PF users hope all is well! I need a reminder of the formulas needed in order to get "Sine of angle of incidence" "Sine of angle of refraction" And "Index of refraction". The only information I have available now is "Angle of incidence" And "Angle of refraction" I'm guessing...
  19. B

    Angular Momentum - rotating rod makes an angle phi with axis

    Homework Statement A thin rod of length l and mass M rotates about a vertical axis through its center with angular velocity ω. The rod makes an angle φ with the rotation axis. Determine the magnitude and direction of L (angular momentum). So we're given: mass - M, length - l, angular velocity...
  20. Martin Hanna

    Finding angle of refraction given angle of incidence?

    Can someone help me in solving this question ? my attemp is sin42/sin 90 to get the refractive index then n =sin i/sin r to get c and for b n=1/sinc
  21. A

    How to solve for angle of reflection in respect to floor?

    Homework Statement A student stands 2.7 m in front of a floor-to-ceiling mirror. Her eyes are 1.64 m above the floor and she holds a flashlight at a distance 0.85 m above he floor. Calculate the angle θ, in degrees, that the flashlight makes with respect to the floor if the light is reflected...
  22. fantisism

    Ice skaters collision with angle

    Homework Statement Two ice skaters crash into each other. Before they collide, one of them (50 kg) is skating in a straight line at 5 m/s, the other (40 kg) is skating at 4 m/s in a straight line at 90 degrees to the 50 kg skater’s direction. After the collision, the 50 kg skater is moving at 4...
  23. D

    Solving a Uniform Beam Inclined at an Angle

    Homework Statement A uniform beam of mass m is inclined at an angle θ to the horizontal. Its upper end (point P) produces a 90° bend in a very rough rope tied to a wall, and its lower end rests on a rough floor (see figure below). Let μs represent the coefficient of static friction between...
  24. prashant singh

    Question from trigonometry -- prove that the largest angle is greater than 120°

    In a triangle whose sides are 3,4 and root 38 metres respectively, prove that the largest angle is greater than 120° My answer: Here angle C > B...(1) and C > A ...(2) adding (1) and (2) we get 2c > A+B, taking sine both side , sin2C = sin(A+B) = sin(C), therefore cosc > (1/2) therefore...
  25. vetgirl1990

    Compton effect: Scattering angle of electron

    Homework Statement A 0.7MeV (E°) photon scatters off a free electron such that the scattering angle of the photon is twice the scattering angle of the electron (θ=2φ). Determine the scattering angle for the electron. Homework Equations λ' - λ° = h/(mec)(1-cosθ) E = hc/λ ρelectron = mev /...
  26. S

    Angle required to hit the target in projectile motion

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  27. Fidelis

    A Finding the Angle Between Two Quaternions: A Simple Solution?

    Hello! I have two quaternions with norm equal to 1. Both are represented in the angle-phase form, i.e, I have q=exp(i*\phi)exp(k*\psi)exp(j*\theta) and p=exp(i*\phi')exp(k*\psi')exp(j*\theta'). Let \alpha be the angle between q and p. I need to write \alpha in function of \phi-\phi', \psi-\psi'...
  28. Jonski

    Finding Angle of Twist at Gear A Relative to Motor

    Homework Statement What is the angle of twist at gear A relative to the motor? (Round to the closest 6th decimal) Homework Equations I know to find the angle its θ = ∑ (TL/JG) but it can also be θ = Lτ/Gr The Attempt at a Solution So i used both these equations, and I got...
  29. S

    Fresnel Loss & Brewster's Angle

    Homework Statement I'm trying to understand these two a bit better in terms of lasers. Fresnel Loss - The loss that occurs when there is a change in refractive index. Some light will be transmitted, while other light will be reflected back into the medium. This is bad for lasers because it...
  30. S

    Engineering Impedance angle in RL and RC circuits

    Homework Statement This isn't so much of a problem itself but I found it interesting that on the All About Circuits website, two of the questions give a phase angle for impedance as opposite the angle of current. I understand the current is 90 degrees out of phase with voltage in both RL and RC...
  31. I

    MHB Angle between two line segments of a cube.

    Given a cube, choose a vertice and draw 2 of the three possible diagonals. What is the measure of the angel between those two diagonals? Proposed answer: We can say that both diagonals touch vertice A, to give it a name. We can also call the endpoints of both diagonals B and C. If we imagine...
  32. G

    Engineering Current phase angle difference (AC circuit)

    Homework Statement Three receivers, with complex impedance \underline{Z_1}=(125+j375)\Omega,\underline{Z_2}=(700+j100)\Omega,\underline{Z_3}=(500-j500)\Omega, and two sinusoidal current generators of effective values I_{g2}=40mA and unknown I_{g1} are connected. When the switch is open...
  33. D

    Why Is the Angle 90-theta in IBNpir^2sin(90-theta)?

    Homework Statement I know the answer to this problem is IBNpir^2sin(90-theta). What I don't get, is why the angle is 90-theta. Homework EquationsThe Attempt at a Solution
  34. O

    How Does Snell's Law Affect Color Dispersion in a Window Pane?

    Homework Statement Dispersion in a window pane. In Figure (a) below , a beam of white light is incident at angle θ1 = 67o on a common window pane (shown in cross section). For the pane's type of glass, the index of refraction for visible light ranges from 1.535 at the blue end of the spectrum...
  35. Blockade

    Can someone help me find the angle between two forces?

    Can someone help me relearn finding the angle between two forces when solving for work of each forces (gravity, tension, fF, normal)? I remember that cos(90°-α) = sin(α) but what I don't understand is when the angle in between is "90°-α" or when it's just "α". I tried doing this on my own and...
  36. Lord Amirul

    How Do You Calculate Cosine Theta from Work, Force, and Distance?

    Homework Statement In the diagram , a block rests on a smooth horizontal surface . It is then pushed with a force of 45 N at an angle of Θ(theta) to the horizontal . 50 J of work has been done to push the block through a distance of 1.60 m Its speed is 2.50 m s^-1. Homework EquationsThe...
  37. Frankenstein19

    Constant force but angle is increased, what happens to work

    Homework Statement A box is dragged a distance d across the floor by a force F which makes an angle theta with the horizontal. If the magnitude of the force is held constant but the angle theta is increased, does the work remain the same, increase, decrease, or first increase and then decrease...
  38. O

    A Angle Trisection: Learn a New Solution Here!

    Hello everyone, i stumbled upon a trisection solution that was unknown to me and looked incredibly great (i am not an expert at all) http://andreasaronsson.com/guides/perspective-drawing/divide-into-equal-parts/ could someone please validate it and explain why it works and why it is not...
  39. chwala

    Finding acute angle between lines/planes and between planes.

    Homework Statement a) Find the acute angle between the line ## r = i+3j+5k+t (2i+4j+k) ## and the plane x-y+z=0 b)Two planes are defined by the equations ## x+2y+z=4## and ## 2x-3y=6 ## i. find the acute angle between them. ii. find a vector equation of their line of...
  40. onemic

    Finding Angle of Inclination With a Given Slope

    Homework Statement Find the angle of inclination of a line when the slope, m, is equal to -1/2 Homework Equations m = rise/run = tan(φ) φ=angle of inclination The Attempt at a Solution I thought the answer would simply be using arctan on the slope, but my answer gives me -26.565051 degrees...
  41. K

    I Function of angle between vector field and scalar function

    I was curious, if you were given a vector field F(x,y,z) = <Fx(x,y,z), Fy(x,y,z), Fz(x,y,z)>, and then some scalar function f(x,y,z), how would you define a function θ(x,y,z) of the angle θ between the scalar function and the vector field at any given point. I know how I would find this at a...
  42. Z

    Which L Bar Orientation Offers Maximum Downward Force Strength?

    Hi All. Given a 20 inch L bar with 1" sides. If 6 inches of this bar is buried in a concrete wall horizontally, which orientation would render the most downward force strength? 1. A V orientation with the tip of the V pointing down. 2. A V orientation with the tip of the V pointing up. 3...
  43. D

    Direction or angle independent image formation in lens

    Is there any way to design a lens or system of lenses where I see the same part of the image, irrespective of direction or angle of view. The light rays can be assumed to be collimated as viewing will be from a distance. Actually- I am looking at focusing on a point or specific area of the...
  44. Frankenstein19

    Find the slope of the tangent at the given angle theta

    Homework Statement Find the slope of the tangent line to the give polar curve at the point specified by the value of theta R = 1/θ, θ=π Homework Equations ##\frac{(dr/dθ)sinθ + rcosθ}{(dr/dθ)cosθ - rsinθ}##The Attempt at a Solution The derivative of r is -1/θ2 Then plugging things into the...
  45. Albert1

    MHB Finding Angle C in Triangle ABC

    $\triangle ABC,\angle B=30^o , \,\,and \,\, \overline{BC}^2 - \overline{AB}^2=\overline{AB}\times \overline{AC}\\ find \,\, \angle C=?$
  46. arpon

    Angle between two straight lines

    Homework Statement Find the angle between the straight lines: ##(x^2+y^2)(\cos^2{\theta} \sin^2{\alpha} + \sin^2{\theta})=(x \tan{\theta} - y \sin{\alpha})^2## Homework Equations [Not applicable] The Attempt at a Solution Dividing by ##x^2##, ## (1+(\frac{y}{x})^2)(\cos^2{\theta}...
  47. ckyborg4

    Is there any relationship between light intensity and angle

    Homework Statement I'm working on a project right now, which uses laser beams and part of the project requires me to find a mathematical model which relates angle of projection to the intensity of the light. Does anyone know of an equation(s) which relates the intensity and angle together...
  48. S

    Angle of average acceleration while turning a curve

    Homework Statement A cyclist is initially heading exactly due North. He then initiates a turn to the West, the turn being a quarter circle with radius 12-m. He travels at a constant speed of 5.5-m/s during the turn. What is the direction of this average acceleration, measured anti-clockwise...
  49. vetgirl1990

    Finding the angle of phase difference - two slit model

    Homework Statement Light of a wavelength 548nm illuminates two slits separated by 0.25mm. At what angle would one find the phase difference between the waves from two slits to be 2 rads? Homework Equations σ / λ = ΔΦ / 2π σ: path difference λ: wavelength Δφ: phase difference The Attempt at a...
  50. N

    MHB Computing height given shadow length and angle of elevation

    Simple geometry can compute the height of an object from the object's shadow length and shadow angle using the formula: tan(angleElevation) = treeHeight / shadowLength. Given the shadow length and angle of elevation, compute the tree height. #include <iostream> #include <cmath> using namespace...
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