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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5
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3answers
178 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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18 views

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
18 views

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
52 views

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
32 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
16 views

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
84 views

extracting Angles from a Rotation Matrix

How to extract the angle a from the rotation matrix, given by: ...
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0answers
12 views

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
107 views

closed form expression for $\sin 10^o$? [closed]

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
32 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
83 views

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
36 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
70 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
99 views

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 ...
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2answers
107 views

Geometry with triangle.

Any other solutions(advice) are welcome. $\angle BAC=60^\circ, \;\;\;\angle ACB=x,\;\;\; \overline {BD}=\overline{BC}=\overline{CE} $
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1answer
44 views

Degree choice in improper integrals resulting in trigonometric functions

people. I have a question regarding the following improper integral, and others like it: $$\int_{-\infty}^\infty \frac{dx}{1+x^2}$$ The end result of that are the two limits: $$\lim_{a\to -\infty} \...
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0answers
48 views

Another variant / corollary of Langleys adventitious angles triangle problem

I recently came across an elegant simple method on Youtube to solve the original Langley's problem using basic geometry principles. Worlds Hardest Easy Geometry problem I have also gone through ...
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1answer
49 views

Quaternion angle calculation

I'm working on a programming project, in this project I'm receiving an angle as a quaternion value, I partially understand how they work but I don't find any math to get the values I need. What I ...
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2answers
76 views

calculating new 3D position on sphere with angular velocity vector

I feel like this is actually pretty simple but still could not find any solutions so far... I'm trying to calculate the movement of a point in a rigid rod with the equation $ \dot P = [ v + \omega \...
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1answer
58 views

Find a point that is perpendicular to line and write it in javascript [closed]

Hi and sorry if my post is not the best but is my first time in something like this I have seen this post, I have two directional points. Point A going to point B. Each point has an X and Y ...
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2answers
53 views

Determine angles of a triangle given lengths of its sides

If I remember correctly this is high school material; I feel ashamed that I can't solve this now. Lengths of a triangle's sides determine its angles; but how to compute these angles?
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2answers
22 views

Rotation of $e_1 \in \mathbb{R}^n$ in angles along the axis

I have the vector $e_1=(1,0,...,0)^T$ in $\mathbb{R}^n$. I would like to rotate it by angle $\theta_2$ along axis $x_2$, resulting in the vector $r_1 = (\cos(\theta_2),\sin(\theta_2),0,...,0)^T$. ...
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1answer
65 views

Angle between vector and x-axis in specific intervals

Given a vector going from a point $(x_0,y_0)$ to $(x_1,y_1)$ in a regular 2D-plane (i.e. an $\hat{x}$-axis pointing right and a $\hat{y}$-axis pointing up), I want to determine the angle between the ...
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0answers
25 views

Curvilinear abscissa = radius * angle - Circular motion

I would like to understand why: $$ s(t) = r \, \theta(t) $$ where $s$ is the curvilinear abscissa, $r$ the radius and $\theta$ the angle in circular motion. Thank you for your time.
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1answer
45 views

how to find slope of discrete point?

I am wondering if it is possible to find the slope at each point in the following dataset, ...
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0answers
25 views

How to know when a 360 rotation was performed around any given axis?

If I have any given axis, e.g. $\frac{1}{\sqrt{2}}\left[ \begin{array}{ccc} 0 & -1 & 1 \end{array} \right]$ and a rotational speed of $\omega = 1.5$ [deg/s] around that axis. How can I check ...
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0answers
119 views

Effect of angle error over distance (error propagation) [closed]

An angle of "$\theta$" has been measured with an error of "$s$" (in degrees). How the position error which is caused by this angle observation error at a distance of "$d$" (in meters) can be estimated?...
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2answers
55 views

Why is this angle not $22.5^\circ$? And does it have an exact value?

Since the angle which splits a square in a half, starting from it's bottom left corner, is $45^\circ$, I intuitively thought that, if I put two squares to be horizontally adjacent, the angle between ...
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1answer
79 views

Why is the sum of all external angles in a convex polygon $360^\circ$ and not $720^\circ$?

Why is the sum of all external angles in a convex polygon $360^\circ$? From my understanding, for each vertex in a convex polygon, there exist exactly $2$ exterior angles corresponding to it, which ...
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1answer
20 views

convex polygon considering three angles

If I choose three vertexes A,B,C in a convex polygon, it so happens that the sum of angleA,angleB,angleC appears to be 180 or larger. Why is this true? I tried drawing the polygon and making triangles,...
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1answer
34 views

Angles of convex polygons

For a convex polygon, show that the sum of any two interior angles is greater than the difference between any two interior angles. (the polygon has more than 3 sides) If I pick 4 dots A,B,C,D and say ...
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1answer
28 views

Defining angle in terms as a limit of ratios of volumes

Let $(\vec{w})^{\varepsilon}$ denote an open ball of radius $\varepsilon$ centered at $\vec{w}$ . The choice of open balls over closed balls is arbitrary. Let $S$ denote a set that's constrained to be ...
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2answers
114 views

geometry question in HK IMO prelim 2018

2018 IMO prelim in HK, Q.3: In triangle ABC, ∠ BAC = 18° and angle ∠BCA = 24°. D is a point on AC such that ∠BDC = 60°. If the bisector of ∠ADB meets AB at E, find ∠BEC. Any form of help will be ...
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1answer
26 views

calculate angle of line with negative slope

I want to use the formula $$ tan(\alpha)=m $$ for negative slopes but always get negative degrees. For instance, say the slope of a line $g$ is $-1$. Using the formula above (arctan$(-1)=\alpha$), I ...
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2answers
45 views

$AB_1$, $AB_2$, $AB_3$ are the altitude, angle bisector, median from vertex $A$ of $\triangle ABC$; arrange lengths $BB_i$ in ascending order

Consider an acute angled triangle $\triangle ABC$ such that $AB\lt AC$. If from $A$ altitude $AB_1$ is drawn, internal angle bisector $AB_2$ is drawn, and median $AB_3$ is drawn. ...
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0answers
35 views

Simply find point in circle border

This seems to silly for you expert guys in math but I am not good in this So Please help. Suppose you have clock of 330 * 330 pixels so I have radius 165 in circle. I want to find position of ...
5
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1answer
119 views

Calculate bevel edge Icosphere

I have an Icosphere with 80 faces, 120 edges. Now i am looking to find out what the angle is of the bevel between all the faces. With the bevel i mean the following see the image below: So i am ...
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1answer
43 views

Bidirectionally of the “Tangent Criterion”

I've recently been reviewing some basic geometry concepts when I saw this one in Evan Chen's fantastic "Euclidean Geometry in Mathematical Olympiads" (EGMO). Proving $(i)\Rightarrow (iii)$ is quite ...
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1answer
148 views

If I square a value units of radians, is the result in units of radians squared or is it still radians?

I am writing a paper on circular motion. A function given is $$T=Msω^2L$$ The units for $ω$ are $\text{rad}/s$. What are the units for $ω^2$? Are they $\text{rad}^2/s^2$ or $\text{rad}/s^2$? If they ...
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1answer
78 views

Internal angles in regular 18-gon

This (seemingly simple) problem is driving me nuts. Find angle $\alpha$ shown in the following regular 18-gon. It was easy to find the angle between pink diagonals ($60^\circ$). And I was able to ...
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0answers
41 views

When the slope of the angle bisector is 1, is the product of the slopes of the 2 lines forming the angle equal to 1

When the slope of the angle bisector is 1, I have been told that the product of the slopes of the 2 lines forming the original angle is 1. Is this true?
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1answer
28 views

Finding the location of points of a triangle given the angle and length ratio.

Given that a point P is located at (-2.5,4.33) I need to locate the points A and B such that $\frac{PA}{PB} = \frac{4.77}{8}$ and $\angle APB = 55^o $. A and B must be on the -ve part of the x axis. ...
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1answer
46 views

Signed angle in plane

What is the formula to compute the signed angle between two vectors $u, v\in\mathbb{R}^2$ where positive angle is equivalent to a counter-clockwise rotation on the plane In other words I would like ...
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0answers
89 views

Orthogonal unit vector in spherical coordinates

A particle is traveling in the direction of the positive $z$ axis, until eventually, it is deflected. The new direction is given by an azimuthal angle (w.r.t. the positive $z$ axis) $\theta$ and a ...
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2answers
41 views

Fast way to compare angles w/o their measures

I need an efficient way to compare the measures of two angles in $\mathbb{R^2}$ that ideally relies on the smallest number of arithmetic operations and no trigonometric operations (no $\arccos$) or ...
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1answer
36 views

Finding sign of an angle without calculating the angle itself

Say we have an angle between vectors $P_1$ and $P_2$ in $\mathbb R^2$ whose vertex, $O$, is at the origin. I would like to know the sign of the smallest signed angle between $P_1$ and $P_2$ such that $...
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2answers
22 views

Prepend a vector with 90 degree angle to an existing one

First of all: my knowledge in mathematics is a bit rusty, so no matter how simple my question is, I afraid I in every case need a somewhat detailed answer: I have a line from coordinates (x1,y1) to (...
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2answers
26 views

Looking for correlation between length and angle

The problem I'm facing might be rather easy to solve, but I can't think of a way how to do it atm. I want to clip straight 90-degree and some other degree lines. If I clip them at a fixed height (like ...