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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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Average direction between two vectors

this is my first time asking a question so I'm sorry in advance for any mistake I might make. So I have 3 points in 3D space: A, B and C. What I want to do is have an object on point B point towards ...
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2answers
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A problem with tetrahedron [on hold]

Let ABCD be a tetrahedron with the property that opposite edges are equal. We know that the angle between the planes ABD and BCD is $90^\circ$ and the angle between (BCD) and (CAD) is $60^\circ$. ...
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1answer
29 views

Mathematical proof regarding angle mirroring

I'm trying to find a proof for a statement that is made in Griffiths' Introduction to Electrodynamics. It can be stated as follows (in my own words): Let $P$ be a point such that its angle in polar ...
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Is there a conformal mapping from the surface of a cube to the surface of a spherical cube that preserves edges?

Is there a conformal mapping (with certain singularities noted below) from the surface of a cube to the surface of a spherical cube that preserves edges? Note that this also implies that vertices and ...
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1answer
34 views

Angle of a Star Inscribed in a Circle

I don't even know where to start on this: In the figure, point O is the center of the circle, points A, B, C, D and E all lie on the circle, and both segment AD and CE go through point O. Angle BEC ...
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0answers
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Triangle Inequality for Angles in Projective Space

I want to show that the angle between two lines through the origin in a (complex or real) inner product vector space $(V,\langle \cdot,\cdot\rangle)$ is a distance function which turns $\mathbb{P}V$, ...
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1answer
14 views

Does a Bijective Commutative transformation on a vector of angles exist?

I have a problem where I have two vectors a and b representing a list of angles. I need to find a transformation T where T(a,b) = T(b,a), where T has a distance metric to compare two transformations,...
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1answer
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Proposition 3.14: Geometry

Please help prove the following proposition: Proposition 3.14 Supplementary angles of congruent angles are congruent. Is this right? (1) Suppose angle ABC is congruent to angle DEF (given) (2) We ...
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2answers
34 views

How to solve this equation using the cosine rule [closed]

How do you do this question using the cosine rule? A triangle $ABC$ has the following lengths: $AB = x$ cm $AC = (x+6)$ cm $BC = (x+4)$ cm $\angle CAB = 60^\circ$ Find the ...
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2answers
36 views

Triangle Geometry question find minumum value of $n-m$

In the triangle shown, for $\angle A$ to be the largest angle of the triangle, it must be that $m<x<n$. What is the least possible value of $n-m$, expressed as a common fraction? I found that $...
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1answer
47 views

Are there two non-congruent quadrilaterals with same sets of sides and angles?

Are there two non-congruent quadrilaterals with same sets of sides and angles? It is relatively easy to construct such pentagons. Trying to construct quadrilaterals allows for seemingly multiple ...
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1answer
17 views

Coordinates of line in sphere with x,y rotation

Lets say that I have a line with one end fixed to the center of a sphere, and the other end can freely rotate. If I were to rotate the line around the x and y axes, what would the coordinates be for ...
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2answers
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Triangle problem, $AC=3$ , $AB=5$ ,…, then $PH=?$

In $\triangle ABC$ : $AC=3$ , $AB=5$ , $\angle ACB= 90 ^ \circ$, $P$ is a point inside $\triangle ABC$ such that $PA+BC=PB+AC=PC+AB$, $H$ is a point on the line $AB$ such that $\angle PHB=90^\circ$ ...
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1answer
29 views

Suspended weight: Representing a vector differently leads to different answers

I'm getting two different answers for the below problem depending on how I represent the relevant vector. My guess is the inverse sine function is affecting things, but I don't understand how I need ...
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1answer
29 views

Confusion the plane bisecting the angle between two given planes containing origin

Suppose, we have two intersecting planes $P: ax+by+cz+d=0$ and $P':a'x+b'y+c'z+d'=0$ where $d, d'$ have same sign. Then the origin lies either in acute angle side(i.e. where the angle between the ...
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1answer
48 views

Maximizing a pool's length

A math project I am doing asks the following: Blammo is to be fired at ground level with a muzzle velocity of $35$ m/s over a flaming wall that is $15$ m high and a ground level shark pool. The pool ...
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1answer
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I need help with a proof for finding an angle measure. [closed]

In a $\triangle ABC$, $AC = BC, \quad \angle ACB = 96°, \quad \angle BAD = 18°$ and $\angle DBA = 30°$. Find the measure of $\angle ACD$. (Without Trigonomety)
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0answers
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How to calculate solid angle of nonspherical surface?

My objective is to calculate (or find an expression) for the solid angle of a circular loop (parametrized by $(x,y)=(r \cos{x_i}, r \cos{y_i})$, where $0\leq x, y \leq 2\pi$) on the surface defined as:...
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1answer
36 views

Is 'turn' a better unit of angular measure?

Radians are generally accepted as natural angular units of measure because they are dimensionless and lead to simple derivatives and series expansions. However, in the modular arithmetic of wavelength,...
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0answers
20 views

angularly and lineraly accelerating particle

Let's say there's this particle that moves with a unit of time. Let's say this particle has a linear velocity and acceleration ($v$ and $a$) and an angular velocity and acceleration ($v_\theta$ and $...
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2answers
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Can there be two adjacent solid angles?

Thanks for reading. My real question is the second part - in the first part I'm just explaining myself. Please read through! Thanks. In 2D geometry, it is easy to picture what it means to add up 2 ...
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1answer
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Need help with angular velocity problem. [closed]

So I have a problem that I just can’t seem to get right and I have only one try remaining. Can someone please help me solve this problem but plz explain if possible. Thanks “Suppose a car runs over ...
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1answer
38 views

How can I find the measure of every angle in a star polygon?

I'm unfamiliar with these kinds of problems. I looked up some formulas and it says for an $(n,3)$ family of star polygons, $\theta = \frac{(1-\frac{6}{n}}{180}$ How do I get these formulas and what ...
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1answer
51 views

Trisecting an angle $\theta$ equally via applying trigonometry

I found an article in a book about trisecting an angle equally. It was written there that Archimedes tried to solve that process by applying pure geometry (using only compass and scale without its ...
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2answers
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Negative Angles

A lot of times text books refer to the measure of angles with a little arrow (see picture below). But to go clockwise they represent it as below. The thing is and maybe this is just me, but I think ...
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1answer
31 views

Find angle of line which runs perpendicular to a tangent trajectory of a point on 2d cartesian frame

As below, I am looking to find the variable '$\theta_e$'. Assuming the parameters which are given are the point ($x,y$) , ($L_h$),($d_e$), v, ($\theta_d$), ($x_d,y_d$). I do not have the parameter '$\...
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1answer
40 views

What is the meaning of an angle, size or shape?

We often use the word angle to mean two different things. First, we use it to mean the something like a “corner” formed by two lines meeting. Second, we use it to mean a measure of how “far apart” the ...
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1answer
24 views

Vector which corresponds to angle between subspaces

The wikipedia article Angles between flats discusses the principal angles between two subspaces of $\mathbb{R}^n$. It states, "if the largest angle is $π / 2$, there is at least one vector in one ...
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2answers
56 views

Find the value of angle using elementary geometry rules

In $\triangle ABC$ with base $AC$, $\angle C$ = $46^\circ$ and $AC$ is extended to point $D$. $E$ is a point on $AB$ and $DE$ is joined. Given that $AB=AD=DE$. Find $\angle ABC$.
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3answers
76 views

Find the $\angle ACB$ of $\triangle ABC$.

If $PC=2BP$, $\angle ABC= 45^\circ$, and $\angle APC=60^\circ$, find $\angle ACB$. All solutions are acceptable but please try solving using reflection of point $C$ through the line segment $AP$. I ...
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2answers
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Intersection of any function and a circle

I wanted to know how to find a specific angle based on a function and a circle intersection. To understand, you first need to see the drawing : What I want is to find the smaller alpha angle ...
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2answers
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Given two angles, exact location of $E$ and $F$ in a square $ABCD$ and diagonal $BD$ intersects $AE$ at $P$. What is the value of $\angle PFC$?

$ABCD$ is a square. $E$ and $F$ are points on $BC$ and $CD$ such that $\angle EAF$ = 45$^\circ$ and $\angle EAB$ = 15$^\circ$. Diagonal of the square $BD$ intersects $AE$ at the point $P$. Than point $...
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1answer
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Solving for the value of $ \angle CEB$ - $\frac{1}{4}$ $\angle CBA$ where $E$ is an exterior point of $\triangle ABC$

From point $A$ of $\triangle ABC$, a line $AD$ parallel to $CB$ is drawn so that $AD=AB$. From point $B$, a line parallel to $AC$ is drawn so that $BE=BC$. Point $D$ and $E$ lie on different sides of ...
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2answers
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Let $ABCD$ be a cyclic convex quadrilateral such that $AD + BC = AB$. Prove that the bisectors of the angles $ADC$ and $BCD$ meet on the line $AB$.

Let $ABCD$ be a cyclic convex quadrilateral such that $AD + BC = AB$. Prove that the bisectors of the angles ADC and BCD meet on the line $AB$. I tried to find similar triangles since the angles are ...
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3answers
169 views

Solve for the angle x?

The problem seems really impossible to me, despite solving many problems on triangles. So I hope that you can solve it. src:https://www.instagram.com/p/BtUNj3IBIW5/
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0answers
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Calculate the area of a parametric sector

I encountered the following definition: $\forall tD_t=\{(x,y)\in R^2:\theta(x,y) \in [-\pi,t]\}$ where $\theta(x,y)$ is the angle in $[-\pi,\pi)$ that the vector $(x,y)$ forms with the x-axis. ...
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1answer
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Understand proofs concerning angles on circles

I am reading the paper "On zeros of convex combination of polynomials" by Fell. In proving a theorem, the author listed two lemmas (Lemma 2 and Lemma 3) without proof. How do we prove the two lemmas?
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1answer
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Two circles with a common tangent

Find the angle $\angle BAC$ in the following picture . My attempt : I tried to apply the relationships in the both circles between different angles and arcs in many ways but it didn't work . Also ...
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1answer
29 views

How to measure an angle in a polygon that is more than 180?

Assume we have an arbitrary polygon that has no holes nor self edge intersections, but can otherwise be concave and deformed. Assume the vertices are ordered either clockwise or ccw. So for example ...
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1answer
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How can I check which face of spherical polyhedron corresponds to a given euler angle?

I am specifically mapping a dodecahedron to a sphere and I am trying to get if a rotator is within the boundaries of a given face. Thank you
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1answer
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extracting Angles from a Rotation Matrix

How to extract the angle a from the rotation matrix, given by: ...
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0answers
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Requirements of 3 proper Euler angles

Why do proper Euler Angles all come in the form of xyx, yzy, xzx, xyx, and etc? Also, why is the third one needed if it rotates around the same axis as the first one? How I'm seeing it right now, each ...
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3answers
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closed form expression for $\sin 10^o$?

As we know that $\sin 15^o$, $\sin 30^o$,$\sin 45^o$ have simple closed form expressions as these are multiples of 3, but i have never seen any simple closed form expression for $\sin 10^o$ or simply ...
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1answer
19 views

Finding a point on a rounded rectangle using an angle

I'm writing an application where I need to be able to plot points onto a rounded rectangle. I know the angle from the center from 0 degrees to where the point needs to be. I need to know the x and y ...
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1answer
25 views

Calculate angle

What angle is between vector a and vector b if the angle between vector p and vector q is 90°, where vector p=5a-2b and vector q=-3a-6b? (Yes this is homework)
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2answers
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What is the value of $\angle x + \angle y$ in the following diagram?

$\angle p=30^\circ$, $\angle q=45^\circ$, $\angle r=50^\circ$, $\angle$ $s=25^\circ$. $\angle x + \angle y = ?$ Source: Bangladesh Math Olympiad 2016 junior Category I could not find any ways to ...
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1answer
28 views

Algorithm for converting a coordinate into angles of a pentagon.

I will go ahead and admit, this might just be something obvious but I did research and couldn't find anything. I have a pentagon, and I know two top points (A & B) and the distance between them (...
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1answer
27 views

Is it possible to calculate the sides of a triangle with the angles and the length from tip to base?

Is there an equation to calculate the length of a triangles sides given only the angles and the length from the tip of the triangle to its base? If so please express the equation using the following ...
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2answers
66 views

Finding out the value of $\angle DQC$ in a trapezium $ABQD$ where $\angle DCB$ = 30$^\circ$

In this below diagram, $\angle ABC=60^\circ, \angle DCB=30^\circ $, $AD$ is parallel to $BC$ and $AP$ is perpendicular to $BC$. Both the area and perimeter of $ABCD$ and $APQD$ are equal . What is the ...
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2answers
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Stuck with a possibly impossible trigonometry question

I need to find the length of the arc between Y1 and Z1 in the image below. If you can even get me to the value of Y, then that will work. I appreciate the drawing may be crude, but imagine that Y and ...