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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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Finding an Angle using Cyclic Quadrilateral and Circle Theorems

To find angle BGE from the diagram above, a proof was proposed: "Angle BCF equals 100 degrees (external to triangle ACB); ADEC and DBFC are cyclic quadrilaterals -> angle ADE equals 100 degrees; ...
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Proof Regarding Tangents

There are two circles: $C1$ and $C2$. They touch internally at point B (note that C1 is inside of C2). C1 has a chord BC, which is produced to meet C2 at D. The tangent from C meets the common tangent ...
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$\cos(a)=4/5$, $\sin(b)=12/13$, 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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$\tan(a) = 3/4$ and $\tan (b) = 5/12$, what is $\cos(a+b)$

It is known that $$\tan(a) = \frac{3}{4}, \:\:\: \tan(b) = \frac{5}{12} $$ with $a,b < \frac{\pi}{2}$. What is $\cos(a+b)$? Attempt : $$ \cos(a+b) = \cos(a) \cos(b) - \sin(a) \sin(b) $$ And we ...
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Which Sign do I choose using the Half Angle Formula for sin for this?

I'm evaluating $\sin\left(\frac{1}{2}\sin^{-1}\left(-\frac{7}{25}\right)\right).$ The first thing I did was rewrite it as $\sin\left(\frac{\beta }{2}\right)$ Then I said that $\sin\left(\beta \...
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Change of reference axis and calculating the coordinates using angle and length

I've got a set of vectors in 2-dimensional coordinate system specified by starting point $(x_0, y_0)$, angle and length. An angle is measured starting on OX axis. So on the graphic below $\alpha \in (...
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86 views

How is an angle's degree determined?

To be as specific as possible I am not asking the following: What is a degree? (Measurement of rotation between two intersecting rays/lines) How much is a degree? ($\frac{1}{360}$th rotation of a ...
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Finding Angle BDF inside a circle

Find Angle BDF What i tried Since Angle AOE is twice Angle ACE, we have Angle ACE= $(360-214)/2=73$ degrees. Angle OET and Angle TAO is $90$ degrees since its a tangent line to the circle. Angle ...
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Why only two dihedral angles for a snub dodecahedron?

The Wikipedia page for the snub dodecahedron provides explicit coordinates for its vertices, from which one can of course by brute force calculate that there are only two dihedral angles. Can anyone ...
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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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Is a single line, line segment, or ray a valid angle?

After online research and several definitions of the term angle it seems they all fit a short set of restrictions for what defines an angle, "a shape formed by two rays that intersect at a point ...
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Can a Point on a Clockwise Circuit that isn't clockwise Increase the Visibility to Other Potential Circuit Points?

Given a fully connected graph of 2-dimensional points: I and a 2-dimensional point G I want to select points from I to create a clockwise circuit around G. Given that I have already selected 2 points:...
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258 views

Name and number of “equilateral tessellations with same angles on all vertexes”

Longer background, shorter questions below: Tessellations of 2D plane consisting of regular polygons are usually described with vertex configurations such as "3.4.6.4" meaning that there are a ...
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Angle between vectors in higher dimensional integral

If I want to calculate a 3D-integral that contains the product of two vectors I can write $\int f(\vec{x}) e^{-i\vec{k}\cdot\vec{x}}\mathrm{d}^3 x = \int f(\vec{x})e^{-ikr\cos{\theta}} r^2\sin{\theta}\...
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How to find angle of arc given arc length and sagitta?

Given the length of an arc and the length of sagitta, can you calculate the angle (radians)? I struggle to work out all the parameters I need. For instance, to calculate the radius I need the length ...
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Incenter of a Triangle.

In triangle ABC, bisectors $AA_1$, $BB_1$ and $CC_1$ of the interior angles are drawn. If $\angle ABC=120^ \circ$, what is the measure of $\angle A_1B_1C_1$ ? I solved this problem as : Mark D, as ...
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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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1answer
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$\Theta =70$ degrees into seven angles $\Theta /7=10$ is not possible by euclids method

Why we can not divide $\Theta =70$ degrees into seven angles $\Theta /7=10$ degrees using euclids tools. How I apply chebyshev polynomial to solve it. Does any one can help, I am not sure how to ...
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55 views

Finding area of triangles inside an isososeles triangle

Hello, I was going through some Olympiad math questions, when I came across this question In $\triangle ABC, AB = AC, \angle A = 120°.$ Points $D, E, F$ are on segments $BC, CA, AB$ respectively ...
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proving that the area of a 2016 sided polygon is an even integer

Let $P$ be a $2016$ sided polygon with all its adjacent sides perpendicular to each other, i.e., all its internal angles are either $90$°or $270$°. If the lengths of its sides are odd integers, prove ...
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1answer
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Using the Properties of Similar triangles and angle properties to find the length AC

Find the length of AC What i tried Since the diagram is a trapezoid, angle $DAB$ is $180-140=40$ degrees. Then using the properties of simillar triangles, angle $DAC$ is equal to angle $CAB$,thus ...
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Why circle is equal to 360 degrees? [duplicate]

A circle is divided into 360 little parts called degrees. Why or how did they choose that figure? Is there a very strong reason for that or it just a accidentally choose.
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Find the angle at which two right circular cone resting on curved surface, touch each other

Two identical right circular cones are resting on their curved surface as shown in the second row of the image above. Let V be the top vertex and O (O') be the center of base circles and A(A') be the ...
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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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0answers
52 views

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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1answer
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Proving that the orthocentre of an acute triangle is its orthic triangle's incentre.

I proved this property with an approach involving vectors. However, there should be a much simpler, elegant geometric proof, probably utilising a bunch of angles. Here is a diagram exemplifying the ...
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Overall angle of addition of two sinusoids with different angles

If $$C\cos(\theta) = A\cos(\theta_1) + B\cos(\theta_2),$$ then how to express $\theta$ in terms of $\theta_1$ and $\theta_2$. I started like $$\mathcal{Re}\left\{e^{j\theta}\right\} = \mathcal{Re}\...
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3answers
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Calculate angles of rectangle

How would one go about to solve the exercise on the image? I really have no ansatz to solve it, except that the triangle with vertices $Z_1, Z_2$ and the point south has the same lengths thus has ...
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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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5answers
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Given a circle of radius r, and two points ('X' and 'Z') on that circle, can some circumcircular arc “XYZ” be constructed of length r?

I am strictly an amateur, not a professional mathematician or some such. This question occurred to me while considering the fact that an angle of 1 radian centered on the center of a circle will ...
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2answers
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Area of Triangle inside a Circle in terms of angle and radius

A circle $O$ is circumscribed around a triangle $ABC$, and its radius is $r$. The angles of the triangle are $\angle CAB = a, \angle ABC = b$ and $\angle ACB = c$. The area $\triangle ABC$ is ...
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Kiselev's Geometry Problem 82

On one side of an Angle A, the segments AB and AC are marked, and on the other side the segments AB' = AB and AC' = AC. Prove that the lines BC' and B'C meet on the bisector of A. My confusion with ...
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Transform data van $0^\circ$ to $360^\circ$ towards $-180^\circ$ to $180^\circ$

I have some data from a glacier surface, for which the aspect ranges from $0^\circ$ (N) to $90^\circ$ (E) to $180^\circ$ (S) to $270^\circ$ (W) to $360^\circ$ (again N). I want to transform these data ...
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Find triangle rectangle opposite side length

In the right-angled triangle below, is it possible to find length $BC$ with only length $AC$ and angle $A$?
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What makes radians superior to turns/revolutions?

1. THE CONTEXT OF THE PROBLEM This question came to me when I was exploring complex exponents. The key identity to computing expressions with complex exponents is the Euler's identity: $$e^{i\theta}=...
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1answer
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Bisector of angle between lines

enter image description here My attempt- (3x-6y-5)/3root(5)=(x+2y-11)/root(5) this gives 3y=7 but both my answer and the correct answer are not matching as well as it says that it contains (1,-3) ...
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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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2answers
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Concurrency (I Think Using Menelaus' Theorem)

Let $ABC$ be a triangle with incenter $I$, and let $B'$ and $C'$ be points on $BC$ such that $\angle{BIB'} = \angle{CIC'} = 90^\circ$. Let $AB'$ meet $CI$ at $P$, and let $AC'$ meet $BI$ at $Q$. Prove ...
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0answers
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Shopper shelf view point calculation with webcam algorithm

Shelf shopper view point Goal: Find the point in the shelf where the shopper is looking at. Based on head pose angles (x,y,z) and left- and right eye (x,y) angles. (yaw,pitch,roll) Given: Shelf ...
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1answer
175 views

For what value on X provides the maximum angle α

In the figure below, what value on X provides the maximum angle α?
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70 views

In a unit circle, what allows the same trigonometric rules to be applied past the first quadrant?

I had previously asked this question and was asked to learn more about the unit circle, which I've done. I now have further questions: When the concept of trigonometric ratios for acute angles is ...
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2answers
173 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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Circle Proof Application Calculation Questions

Question 1-Circle I look this question up on the internet and found out that the answer was 58, but could someone please explain how to get to the answer? I know that the angle is 46 degrees, so I ...
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Basic vectors question [closed]

The components of a vector along $x$ and $y$ directions are $(n+1)$ and $1$ respectively. If the $xy$ coordinate system is rotated by an angle $θ=60°$ then the components change to $n$ and $3$. The ...
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318 views

Making a regular tetrahedron out of concrete

I'm trying to make the following tetrahedron made of concrete just for fun: Each edge is a beam with a triangular cross section. I imagine the easiest way is to make 6 identical truncated triangular ...
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1answer
127 views

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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1answer
242 views

Find distance from center of equilateral triangle to edge in given angle

I need to find the distance from the barycenter of an equilateral triangle to the edge in a given angle. Here's a little sketch: Given the outer radius of the triangle, the angle and the rotation (...
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115 views

How significant is the difference between averaging angles and averaging unit vectors?

I understand that numerically averaging angles (which I will call the $shortcut$ average for convenience) is in general going to produce a very different result than converting to cartesian unit ...
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1answer
63 views

General equation/function to get angle from x and y coordinates?

We can get the angle between $x$ and $y$ (or $\cos{\theta}$ and $\sin{\theta}$ respectively) from $$ \theta =\tan^{-1}{\frac{y}{x}} $$ but only if $ -\frac{\pi}{2} < \theta < \frac{\pi}{2} $ ...
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Calculate the angle enclosed two lines by means of the scalar product

What is the angle between a side and the diagonal of the unit square? what is the angle between the body diagonal and a touching edge of an n-dimensional unit hypercube?