Questions tagged [angle]

An object formed by two rays joining at a common point, or a measure of rotation. In the latter form, it is commonly in degrees or radians. Please do not use this tag just because an angle is involved in the question/attempt; use it for questions where the main concern is about angles. This tag can also be used alongside (geometry).

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What is the angle from (0,0) to (longitude, latitude)?

Starting on the crossing between the equator and the Greenwich meridian (0,0), one can proceed to any point on Earth with a given longitude and latitude along a great circle. Seen from the centre of ...
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Calculate new point of line when changing the angle

I got 3 Points which form an angle alpha. How do i calculate the new location of Point3 when the alpha is changed? Point1 and Point2 stay staionary.
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Geometry of angular variables

Angular variables have an interesting property in that for some applications, e.g. angle at which the light beam of a lighthouse is pointing, we expect some functions of that variable to not depend on ...
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Compute the angle of the tangent line to space defined by a curve

I"m taking multivariable calculus and I'm being given the curve $\vec{r}(t)= e^t \textbf{i} + (cos^2t + 1) \textbf{j} + (-t^2 + t - 1) \textbf{k}$, the point $P_0 = \vec{r}(0)$ and the yz-plane. I ...
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315 views

How to determine Euler angles of ZYZ rotations?

Consider a point $\mathbf{P}=(x \ y \ z)^\text{T}$ which is transformed into $\mathbf{P'}=(x' \ y' \ z')^\text{T}$ in counterclockwise direction according to the ZYZ convention as follows: $\begin{...
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Find angle of which a cannon of fixed length has to fire

A cannon is firing at a target $(x, y)$ units away. The length of the cannon is $l$, which determines the origin point of the cannonball along with $\theta$. The linear speed of which the cannonball ...
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604 views

Finding the angle between two points given their Azimuth and Elevation angles

I have two points in the sky and I have their coordinates in Azimuth and Elevation angles with respect to position O. I want to find the scalar angle between the two points w.r.t. position O. Thank ...
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Using the definition of inner product to find the axis of rotation about a line

Let's begin with the definition of the inner product. It's as follows: $$ A . B = ||A|| \ ||B||\cos(\theta) . $$ My understanding is that the $\theta$ is the angle between the two vectors. As ...
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How can you find the degrees of a curved line's corners by graphing a vertical and horizontal line?

Sorry if my title appears subjective I am sure there is a more technical term for what I am asking. Maybe the image will explain my question better.
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How to flatten out a curve based on the dot product to be linear?

I am interpreting a value based on the amount an object is "facing" a wall in a performance critical computer simulation. I take the dot product between the object's forward vector and the negated ...
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101 views

How to calculate missing point of triangle?

I am about to develop a special animation where I want to rotate a triangle (given a specific width angle) around a circle (given a specific radius) given a specific rotationAngle. This is how I can ...
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1answer
85 views

$\cos(a)=4/5$, $\sin(b)=12/13$, what is $\sin(c)$?

$\cos(a)=4/5$, $\sin(b)=12/13$, what is $\sin(c)$? with $a,b,c < \frac{\pi}{2}$. Attempt : Since $\sin^{2}(a) = 1 - \cos^{2}(a)$, I get $\sin(a) = \frac{3}{5}$. But how to get $\sin(c)$? I have ...
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How to create a point behind another point given an angle?

I have a point A and a radian angle value R (image below describes this heading system) that represents a heading from point A. How do I create a point B that is a small, fixed distance (like 1.0 ...
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79 views

I found a weird occurrence with equal angle polygons and sine waves and i need help proving it

Here is a desmos graph that visualizes what I am about to say Okay, let's say we have a polygon with $s$ sides and $a = \frac{360°}{s}$. All of those polygon's angles are equal and all of it's sides ...
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Color wheel in the complex plane

Is it possible to arrange the colors of the color wheel on the unit circle in the complex plane such that mixing any two colors results in the color corresponding to the product of the two ...
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Minimum angle at points for every possible polygon

Given a point set $S$ in 2-dimensional space, one can generate a multitude of possible polygons with a vertex at each point $s_i \in S$. I'm working on the problem of finding such a polygon with ...
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What happens to angle between vectors through base transformation?

I am currently working with vectors in $\mathbb{R}$^2. For my specific project, it is beneficial to identify a non-standard basis as "new standard basis" of $\mathbb{R}$^2. For example, instead of ...
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1answer
33 views

Formulating relation for calculating distance

Assuming that the person stands parallel to a wall. The person and the wall are at the same ground level. The person takes a picture of the wall (Considering that the person always captures the bottom ...
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274 views

Finding angle between 2 vectors using inner product

Consider $\mathbb{R}^3$ equipped with the inner product $$ \langle u,v\rangle = u_1v_1 + 2u_2v_2 + 3u_3v_3 $$ Let $$ a = \pmatrix{2 \\ 1 \\ -4} ~~~~\mbox{and}~~~~ b = \pmatrix{1 \\ -1 \\ 3} $$ ...
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find the angle in a triangle with angles $ 20^{\circ}, 70^\circ, 90^\circ $

I have triangle geometry problem: a) Let $\triangle ABC$ be a right triangle with $\angle A=90^\circ$ and $\angle B=20^\circ$. Let BE be the angle bisector of $\angle B$, and $F$ be a point on ...
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136 views

Combining two angles in a specific way to find a third angle?

You are given an arbitrary angle $h$. It can be any angle from $0^\circ$ to $360^\circ$. You are also given an angle $v$, which is guaranteed to be between $-90^\circ$ and $90^\circ$. Find angle $a$ ...
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Why square r when duplicating an angle?

I am wondering if this is just a feature of complex numbers or a general geometric/vector requirement. But even if it is that way, cam you give a rationale and explain the logic behind it?
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Finding length of diagonal in compound shape, cuboid and rectangle based pyramid

How to find the length of diagonal and the angle? Thank you.
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difference between turning angle and heading angle random walk, how to calculate the former

I would like to know which is the difference between a turning angle and a head angle, I ask this since I am trying to estimate the parameters from data in the context of a random walk. Any suggestion ...
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82 views

Why does dot product give correct angle, but cross product does not?

Question: The primitive lattice vectors for a body-centered cubic lattice are given by $\vec a_1 =\frac{a}{2}(1,1,-1)$ , $\vec a_2 =\frac{a}{2}(-1,1,1)$ , $ \vec a_3 =\frac{a}{2}(1,-1,1)$. Calculate ...
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What do “mod $2x$” and “mod $x$” mean when used with angles?

I do not understand what the notation "$\operatorname{mod}{2x}$" or "$\operatorname{mod}{x}$" means in a geometric proof involving angles. I need to understand a proof of a lemma about the ...
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1answer
38 views

Distance between a plane and a point on a line

I have a line that is angled .2 deg off from the plane. I would like to calculate how far the distance is between the plane(a) and line(b) at any given point (c).
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443 views

Circle bounce off circle direction

I'm making a game in c# where i need a circle to bounce off of another circle, the circle always travels the same speed and there is no gravity so i only need to know the direction at which the circle ...
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1answer
30 views

Angle to bypass circle at n distance and direction

Forgive me if this is rather basic (I never did trig!). I'd like to work out the red angle in the picture below, assuming the black dot is n distance from the circle. It could also be in a different ...
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1answer
488 views

Trying to prove corresponding angles are equal in case of parallel lines

I was trying to find/generate a proof that proves equality of corresponding angles: Example 1 (keeping above figure in mind) we can safely say that the angle between the two lines will change only ...
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3answers
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Determine what is the angle of an complex number without imaginary value

Okay, so this is bugging me now. I know this: while tg angle = Y / X for y > 0, angle is an element of < 0, PI > for y < 0, angle is an element of < PI, 2PI > for y = 0, angle is 0 or PI ...
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709 views

Does direction of angle (clockwise/ anticlockwise) matters in trigonometry

In a Cartesian coordinate system, we draw a unit radius arc with centre at origin in anticlockwise direction. Let the angle substended by this arc be $\theta$. Now if we measure this same $\theta$ in ...
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How to prove that $ \bar e_2 = e_1 \sin (w) + e_2 \cos(w)$ where $w$ is the angle between $e_1$ and $e_2$

In the book of Linear Algebra by Werner Greub, at page 201, it is asked that Consider an oriented inner product space of dimension 2. Given two positive orthonormal bases $e_1, e_2$ and $\bar e_1,...
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Find clock time, given lines of hands

I have a clock, and two hands for minutes and hours. Clock is centered somewhere around (165, -163) I have two lines, represented by two points each. To be specific: (51, -143) and (173, -158) for ...
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70 views

How do I get the exit angle of a body?

I have a 3D environment with vectors $(x, y, z)$. For example: Room size $10 \times 10 \times 10$ Bulb in the position $(3,5,10)$ Measuring points: $(5,5,0), (1,1,0), (5, 0, 5)$, etc. A light bulb ...
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Calculation of triangles side B if I know the angles and side a?

How do I calculate the side B of the triangle if I know the following: Side $A = 15 \rm {cm} ;\beta = 12^{\circ} ;\gamma= 90^{\circ} ;\alpha = 78^{\circ} $ Thank you.
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Simple? 3D geometry question

I want to grind a specific front angle on a piece of metal in the horizontal plane while at the same time having a specific secondary angle in the vertical plane. If I present the workpiece at, for ...
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286 views

Find area of circle without sector but with triangle: Do not use trigonometry

How to do this without using trigonometry please? A sheep is tethered to a post which is 6 m from a long fence. The length of rope is 9 m. Find the area which the sheep can feed on. Let the post ...
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Rotate a curve to match a model curve

I have a given curve which could be in any direction and I have a model curve which is fixed,I have find the angle by which I have to rotate the moving curve so that it matches the fixed curve I ...
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Find a shoot angle looking at a photograph

Is there a way to find which anlges a photograph is shoot from? Using a protractor or some other tool. At least for objects which we can say are staying at right angle. For example for an item on a ...
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Finding length of line where angle bisector meets line

Say triangle $ABC$ has a right angle at $B$, where $AB=1$ and $BC=2$. The bisector of angle $BAC$ meets $BC$ at $D$. Find a length of $BD$. I seem to have forgot the property that would help me solve ...
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(zooming on cluster of points in (2D)- calculate Z coord. for which α = β

I am writing a script which zooms a camera on a given object (set of points in 3D). I have to take perspective into account (the further a point on the object is from the camera, the smaller it ...
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Calculating intersecting angles from headings on a -180 to 180 degree plot

I’m trying to program an agent to avoid barriers that it hits. I have access to the heading of the agent as it meets the barrier, which are recorded in positive and negative degrees up to 180 (as ...
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Plot the line in the plane z=3 that makes an angle of $\pi/6$ radians with $\hat{i}$ and an angle of $\pi/3$ radians with $\hat{j}$

I'm not sure how we measure the angle between i-hat and the line and j-hat and the line. i-hat and j-hat are perpendicular to each other They are axis, x and y axis respectively. Therefore, I don't ...
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Prove the exterior angle bisectors are equal

Imagine a triangle with angles 132,36,12 I draw the exterior angles bisectors (132 and 12) I want to prove that these bisectors are equal... Please take a look to the figure I want to prove that AM'=...
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1answer
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Calculating supplementary angles from intersecting line with direction and line with gradient

Example image where I'd be interested in finding angles a and bA simulated robotic agent is travelling in an known direction heading relative to north as it hits (at for example, 30 degrees) a ...
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126 views

Finding closest point to a direction vector

I got an array of 3D points $(x, y, z)$ and a "Rotator" object (pitch yaw roll). Assuming the Rotator location is in $(0, 0, 0)$ I'm looking to find the closest point to the direction my Rotator ...
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163 views

Pool billard ball route function (the angle of reflection is equal to the angle of incidence)

Recently I have found an exercise for algorithmics students, in which I have to implement algorithm, which will calculate the ball route after hit and return specific destination pocket or word "None" ...
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1answer
81 views

Right triangle problem involving circle

What is the length of line X and line Y such that, together with line B, they form a right triangle? Note: -the vertex between line X and line Y should be a point in the circle -the angle between ...
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166 views

Force axis while finding optimal rotation using singular value decomposition?

I'm using the method from here to obtain a transformation matrix with optimal rotations given two sets of 3D points: http://nghiaho.com/?page_id=671 So far so good. I can extract Euler angles from ...