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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Angle of a triangle in a cube

Find the angle of a triangle in a cube. I don't how to start on this problem. The only I have noticed is that it may be a isosceles triangle so the two angle should be the same. Can somebody give me ...
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Calculate the distance of any point on the arc from the center of circle

This is my first time posting so I hope my formatting is correct. Consider this, I have two circles, one big one small with radius $r_1$ and $r_2$. The borders of both circles are touching. See image: ...
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1answer
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Best way to describe the angle from another ray on a circle [closed]

What I have is $3$ rays each of whose origin is the same. Ray $Z$ is always $0^{\circ}$ and ray $X$ and ray $Y$ is a random angle away from ray $Z$ in a clockwise direction. What is the best way to ...
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How can I show that the angle between any two categorical points is between [0°,90°]? [closed]

I'm currently studying Bivariate Analysis of categorical values, but I don't know how to answer this question.
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How to get the opposite angle?

I have been looking for the answer to this question but I haven’t found anything related. I will use the following image as an example. As you can see, there is a circle divided in different parts of ...
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Substituting the Angle Between Two Complex Vectors to Vector Product Addition

As in this paper, the angle between two complex vectors $u,v\in\mathbb{C}$ may be taken as: $$ \cos(\theta)=\frac{\text{Re}(u\cdot v)}{|u\cdot v|}, $$ where $\text{Re}$ takes the real part of the dot ...
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How many angles can be drawn using only a ruler and a compass?

So far I know that it’s possible to draw angles which are multiples of 15° (ex. 15°, 30°, 45° etc.). Could anybody please tell me if it's possible to draw other angles which are not multiples of 15° ...
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In triangle $\triangle ABC$, angle $\angle B$ is equal to $60^\circ$; bisectors $AD$ and $CE$ intersect at point $O$. Prove that $OD=OE$.

In triangle $\triangle ABC$, angle $\angle B$ is equal to $60^{\circ}$; bisectors $AD$ and $CE$ intersect at point $O$. Prove that $OD=OE$. So I've already made a diagram(it is attached below), but I ...
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The bisector of the exterior angle at vertex C of triangle ABC intersects the circumscribed circle at point D. Prove that AD=BD

The bisector of the exterior angle at vertex $C$ of triangle $ABC$ intersects the circumscribed circle at point $D$. Prove that $AD=BD$. So what I'm wondering is how to prove this? I've already drawn ...
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Mixtilinears and Symmedians

(this is from EGMO) Prove that angles ATK and LTI are equal. The hint in the book was about symmedians. I am not sure how to prove that line segment AT is the T symmedian, angle chasing did not work, ...
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Find the angle θ (all the circles are tangent)

In the following figure ABCD is a side square $\alpha$, the points $P_0, P_1, P_2, P_3, Q_0, Q_1, Q_2, Q_3, X \ and \ Y$ are points of tangency, $BC \ and \ ZB$ are the diameters, respectively, of the ...
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1answer
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Proving an approximate angle trisection by compass and straightedge

My 70 year old father has given the below explanation. Can some one please verify or point out deficiencies if any. The geometrical problem of trisecting any given angle by using compass and a ...
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Angle Proof Inside Circle

The vertex of angle $\angle BAC$ lies inside of a circle. Prove that the value of angle $\angle BAC$ is equal to half the sum of angle measures of the arcs of the circle confined inside angle itself ...
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1answer
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Proving that two segments have same length. [closed]

Let $AL$ and $BK$ be angle bisectors in the non-isosceles triangle $ABC$, with $L$ situated on the side $BC$ and $K$ situated on the side $AC$. The perpendicular bisector of $BK$ intersects the line $...
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Distribution of an angle between 3 normally distributed 2D points

Example image Given 3 normally distributed points in 2D space, what would the distribution of the angle $\alpha$ between the three points be & can it be reasonably well approximated with a (...
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Divide a given $1/7$th of the full angle into (1) three congruent parts (2) five congruent parts.

The problem is from Kiselev's Geometry exercise 484: Divide a given angle congruent to 1/7th of the full angle into: (1) three congruent parts; (2) five congruent parts. What I know is that, as ...
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apply arcos to out of domain $[-1, 1]$ values, such that -1.02

I do apologise if the problem sounds a bit confusing, it's not a complicated question, I will make it short as possible. I am trying to archive an ellipse parameterisation, with a reference to SVG ...
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What is the possible line of reasoning/motivation that led to the present definition of radians?

I know this might sound like a silly question at first. Let me elaborate. What I mean by 'line of reasoning; here is what the person who defined radians the way they are defined thought to arrive at ...
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Proof verification that $t(n+1)=t(n) + \pi$ using mathematical induction

I am beginning to learn how to write proofs and I would like some verification on this simple proof I have done for the sum of the interior angles of a polygon. I thought this would be a good one to ...
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What are the implications of the fact that radian measures of angles are real numbers?

Let's say that we proved that the radian measures of angles are real numbers (i.e. if we have an angle $x \text{ rads}$, then $x \in \Bbb R$) since the radian measure of an angle $\theta$ is the ...
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Simplify $\tan^{-1} ( \frac{x-\sqrt{1-x^2}}{x+\sqrt{1-x^2}} )$ with trigonometric substitution

I will explain my approach, help me with the last step please! $$ \tan^{-1} {\left(\frac {x - \sqrt {1-x^2}}{x + \sqrt {1-x^2}}\right)}$$ substituting x = $\sin \theta$ (as learnt from book) and ...
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What exactly is a constant angle?

I previously asked a question about what a non constant angle is but it was closed due to lack of clarity and hence, I'm posting a new question. The notation $x^c$ will be used in this question to ...
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Why are radians treated like a quantity while degrees are treated like a unit?

According to this answer about using Euler's Identity in Degrees, radians and degrees are interchangeable. Why is it that:$$(e^i)^{\pi/2}=i=(e^i)^{90^\circ}$$ But: $$i^{2/\pi}\neq i^{1/90}$$ Edit: ...
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in the triangle ABC on the AC side, points M and N are chosen such that ABM = MBN = NBC

in the triangle ABC on the AC side, points M and N are chosen such that <ABM = <MBN = <NBC It turned out that NB = BC. On the side AB, a point K was marked such that BK = BM. Prove that AK + ...
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Can we construct $142$ degrees and $172$ degrees by using only straightedge and compass?

Can we construct $142$ degrees and $172$ degrees by using only straightedge and compass? I already tried rewrite $142$ to get some angles that can be constructed , such as $90$,$45$,$60$,$30$,$15$,$...
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Calculate the angle of $\theta$ in pythagoreans theorem with different units for the Adjacent and Opposite sides

In the above image I know the value of the adjacent side. It's $298$. I know the value of the opposite side it's $806.8$. The problem is $298$ is in units of 'bars' on a stock chart and the value ...
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How to measure the angle between two parallel lines?

In some geometries, parallel lines "meet/touch/coincide" at infinity. This being the case, there must necessarily be an angle between them. I was wondering what the "value" of this ...
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29 views

Find an angle created by lateral edge and the base of the Pyramid

Pyramid $SABC$ has right triangular base $ABC$, with $\angle{ABC}=90^\circ$. Sides $AB = \sqrt3, BC = 3$. Lateral lengths are equal and are equal to $2$. Find the angle created by lateral length and ...
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If $|z|^2+\bar{A}z^2+A(\bar{z})^2+B\bar{z}+\bar{B}z+c=0$ represents a pair of intersecting lines… find the value of $|A|$.

If $|z|^2+\bar{A}z^2+A(\bar{z})^2+B\bar{z}+\bar{B}z+c=0$ represents a pair of intersecting lines with angle of intersection $'\theta'$ then find the value of |A|. I tried using general equation of ...
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How to characterize the angle of a vector with the same angle to each of a set of vectors

Suppose I have a set of $k$ linearly independent vectors $V\subset\mathbb{R}^k$ embedded in $d$-dimensional space, $d > k$. I want to find a vector $x\in\mathbb{R}^d$ and constant $c$ such that $\...
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2answers
219 views

Coordinate proof that the sum of a triangle's angles is $180^\circ$?

I was answering a question about why the Penrose triangle is impossible when I realized I haven't seen a coordinate proof that the angles of a triangle in $\mathbb{R}^n$ add up to $180^\circ$. I know ...
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Question about alternative interior angles

The source given mentions that $c$ and $f$ are alternative interior angles. Why $c$ and $d$ are not alternative interior angles? They should be because they are both on the opposite sides of the ...
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Part Angle from 2 Camera Views

I am attempting to calculate the angle of a part that is being viewed from two cameras positioned at 90 degrees. Based on the picture captured from both cameras, I am able to determine the angle of ...
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Is there an unambiguous composable representation of gimbal orientation?

There are multiple ways to represent orientation: A rotation matrix, A quaternion, A triple of angles (Euler or Tait-Bryan). Of these, the latter option has two possible representations for each ...
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1answer
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How to find Theta 1 and theta 2 inverse of the two line connecting [closed]

I'm doing the two axis arm robotics on the canvas which shown in the picture as red to blue circle is theta 1 and than blue to yellow is theta 2 here i need to find joint pair of them which is inverse ...
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angle between two 3d structures

I want to know the angle between a 3d structure and a solid plate. The 3d structure is here. Please give me an idea what points should I take to construct the plane for the 3d structure and use ...
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Trigonometry value problem [closed]

Given that the acute angle $x$ is such that $\sin x = \frac 1 3$, find, without the use of a calculator, the exact value of $sin \frac x 2$.
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How to find the angle of a non right angled triangle in a cube?

I have to find $\angle MHN$ ($\angle H$ in $\Delta HMN$). It is inside a cube that has side lengths of $12$ cm. $M$ is the midpoint of the diagonal $BD$ and $N$ is the midpoint of edge $GF$. Here's ...
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How do I prove both arcs are equal? [closed]

As in the following image, the segments AD, DB, BE and EC make the same angle (x) relative to the diameter of the circle QP. How can I prove the arcs L1 (AB) and L2 (BC) are equal?
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Fit an object inside a Camera Field of View (FOV)

I'm developing a game in which I want to focus a camera to fit an object entirely in its Field of View (FOV). The Camera FOV angle is 70 degrees. So I need to find best the distance between the camera ...
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Finding angle between two hexagonal planes

I am looking to get angle between two hexagonal planes. I have coordinates of all 12 vertices (2 hexagons). Is there anyway I can find the angle between the planes. And also I have the information ...
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Measuring the Angle of a Triangle with a Protractor (Question Illustrated by Image)

Forgive my ignorance, and teach me the correct way to read an angle when I am using a protractor. From the image below, would any of the two statements below be correct? If yes, which one? If neither, ...
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Problem regarding the intersection of a circumscribed circle and an exterior angle bisector and the midpoint of an arc

In the very beginning, I'm going to refer to a very similar question where, unlike in my task, there is an assumption the intersection of the exterior angle bisector and a circumscribed circle is the ...
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Reflect an angle around an arbitrary axis.

What is the formula to reflect an angle around an arbitrary axis? Let D be an arbitrary angle rotated counter-clockwise from the x-axis. Let ...
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25 views

equal angles or maybe circle segment

in the attached picture you can see a red and a blue line. The red line is given (but it could also be looking different, hence the second example). The points Pstart p1', p2', p3' and Pend are given. ...
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1answer
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Elementary Geometry : Structure of presentation

I will have a presentation on elementary geometry, and more precisely on the straight line and the triangle. The presentation should be in the university, in front of the fellow students. For this I ...
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1answer
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Problem with $a\sin(x)+b\cos(x)=\pm\sqrt{a^2+b^2}\sin\left(\arctan\left(\frac{b}{a}\right)+x \right) $

Consider $f(x)=a\sin(x)+b\cos(x)$ where $a,b$ are some real constants. Putting $f(x)=R\sin(\alpha+x)$, I got $$f(x)=\pm\sqrt{a^2+b^2}\sin\left(\arctan\left(\frac{b}{a}\right)+x \right) \tag{1}$$ ...
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1answer
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Inclination angle with respect to a plane

I have performed some molecular dynamics simulation and outcome gives position of each atom in Cartesian coordinate system. The outcome looking like this, where the yellow atoms some sort of liquid ...
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Correct interpretation of “A ray of light makes an angle of $10^\circ$ with the horizontal above it”

I encountered this problem in Physics and the direction chosen by me was different from that used in the answer hence I got the wrong answer. The problem here is in the mathematical interpretation of ...
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What is this ' +°" ' direction?

I have looked all over google for this and I cannot find it because I don't know what it is called, but here is an example: Azimuth: +283°14'39" What is this called? Also, is this some way to ...

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