# 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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### How to convert Cartesian coordinate to polar coordinate in $-180°$ to $+180°$

I wanted to plot temperature at circumference of a circle. I extracted the data by converting cartesian coordinates into polar coordinates by using ATAN2 function, but the plot is having negative and ...
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### If the length $BC=l$, length of arc $AB=l_1$ and length of arc $AC=l_2$, then $l+l_1+l_2=$

Question: A circle with centre $C_1$ and radius $\frac32$ touches another circle with centre $C_2$ and radius $\frac12$ externally at point $A$. A common tangent touches circle with centre $C_1$ at B ...
1 vote
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### Calculating $ACB = A'CB'$ given that $ABC$ and $A'B'C$ are equal in area

Given is a triangle $ABC$ with incircle center $I$ and side centers of $AC$ and $BC$ being named $M_a$ and $M_b$, respectively. Let the intersection of the lines $M_bI$ and $BC$ be called $B'$ and ...
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### Geometry: In the $\triangle ABC, AB=8, BC=7, CA=6$. Let $E$ be a point on $BC$.

In the $\triangle ABC, AB=8, BC=7, CA=6$. Let $E$ be a point on $BC$ such that $\angle BAE=3\angle EAC$. Find $\frac{4(AE)^2}{5}$. In my solution I had started with the apollonius's theorem which ...
1 vote
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### How to swap the roll and pitch of a quaternion

I'm writing code that receives quaternion values that are used to rotate a $3$D model. To display the model with the correct orientation, though, I'll need to swap the roll and pitch (rotation about ...
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### Perpendicularity in a given triangle

I was asked to solve the following problem by a friend: Here, $BC$ is a diameter of the circle, $E$ is the midpoint of the $DC$ arc, $F$ is the midpoint of $BD$, $G$ is the intersection of $FE$ with ...
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### Geometry question on angle chasing concerning 3 squares

I am kind of stuck on this problem. We know that the 9 points present in this sketch form three squares, HBAI, CFGB and DEFC. We also know, that the lines DI and AF intersect in S. The question for ...
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### How do we define exterior angle of a concave polygon whose interior is reflex?

How do we define exterior angle of a concave polygon whose interior is reflex? I have seen in few books and websites saying that, sum of all exterior angles of a concave polygon is $360$ degrees. ...
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### Oriented area of a spherical triangle?

I want to know if there is a way to switch between the inner and outer areas of a sphere triangle based on the orientation of the vectors that make it. For example let's see this picture: If $A$ is ...
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### Does exterior angle bisector theorem hold for every non-equilateral triangle?

I'm a high school student and I had this theorem in my book:- The external bisector of an angle of a triangle divides the opposite side externally in the ratio of the sides containing angle. Now this ...
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### Show that the quadrilateral $BCED$ is inscribed...

Problem The triangle $ABC$, with $AB>AC$ and $\angle A \neq 90$, is inscribed with a center circle $O$, and $T$ is the diametrical point opposite $A$. The tangent in $T$ to the circle intersects ...
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### Find the ratio of the perimeter of a square and of a triangle.

Problem: Let the square $ABCD$ be on the side $l$ and the points $E$ and $F$ on the sides $BC$ and $CD$ respectively so that $\angle EAF= 45$. Find the ratio between the perimeter of the square and ...
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### Two perpendicular diameters $AB$ and $CD$ are considered on a circle. Let $M$ be a point on $BC$. Prove that $AN=MN+MB$.

Problem Two perpendicular diameters $AB$ and $CD$ are considered on a circle with centre $O$. Let $M$ be a point on the small arc $BC$. The parallel drawn through $O$ to $MD$ intersects $AM$ in $N$. ...
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### What's wrong with the angle trisection using Intercept theorem?

Could anyone tell what I'm missing? I know that angle trisection is proven to be impossible (see Pierre Wantzel in https://en.wikipedia.org/wiki/Angle_trisection). However, I just came up with the ...
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### Answer with no trigonometry... Let $\triangle ABC$ be isosceles with $AB=AC$. Let $D$ such that $BD=AD$. Calculate the angles of the triangle $AED$.

PROBLEM Let $\triangle ABC$ be isosceles with $AB=AC$. On the extension of side $BC$, a point $D$ is considered such that $C$ belongs to side $BD$ and $BD=AD$. If the bisector $\angle ACD$ forms with ...
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### Convert angle to value and value to angle

I have an "arc" react component and I'm struggling with the math to convert the angle (in degrees) to a value, and the value to an angle. This arc has a "handle" which represents a ...
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### proving angle formed by simson line equals another angle

P is a point on the circumcircle of $\triangle{ABC}$ and $O$ is its circumcentre. Prove that $\angle{APO} =$ the angle between the Simson line of $P$ and $BC$. Here's a diagram I drew on geogebra of ...
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### Triangle apparently has two equivalent angles, but not really [closed]

What angles are ${a, b, c, d}$? As far as I know, $a = 180^\circ - 130^\circ = 50^\circ$, however, I expected $c$ to be the same as $a$ and it's not, according to cimt.org.uk. (Figure from cimt.org.uk)...
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### Is it possible to calculate the angle between two observers given their angles to three of the same points?

Given the image below, is it possible to calculate the angles E and/or F given the angles $A,B,C$ and $D$? The situation is as follows: Two observers each measure the angle between point $1$ and ...
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### 2D histogram of angles between vectors and a fixed vector

I am looking at the orientation of molecules with respect to an interface as a function of their distance from the interface. The molecules are approximately linear, so I measure the angle theta ...
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### Is it possible to find $\angle BAO$ given two additional pieces of information?

Figure 1 with Answer Choices This is a GMAT practice question that I cannot solve. The correct answer states that the angle can be known with either piece of additional information, but I cannot see ...
1 vote
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### Software to simulate angles in a pv system

I am trying to model a pv system and I want to simulate different angles, and to calculate values of different angles. I am asking if there is any software that allows me to design the figure below ...
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### How do I calculate the parabola of a molotov with only angle and distance?

I am playing a game where you can shoot a molotov. My goal is to be able to choose a distance I want the molotov to land (from the player) and get an angle to aim to reach that, the game has no ...
1 vote
22 views

### Euler angles to ENU coordinates

Given the LLA coordinates and Euler angles (orientation) of a phone, where alpha = beta = gamma = 0 when the top of the phone is pointing north and facing up, I would like to find the unit ENU ...
1 vote
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### Angle Chasing in a convex quadrilateral

Find the measures of the angles of the convex quadrilateral ABCD, if $\angle ACD = 78°$ , $\angle BDC = 22°$, $\angle CBD = 12°$ and $\angle CAD = 24°$. Source: Romanian Mathematical Gazette
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### $M$ is inside the parallelogram $ABCD$. If $\angle MBA=\angle MDA$, then $\angle MAB = \angle MCB$ [closed]

Let M be a point inside the parallelogram ABCD, such that $\angle MBA = \angle MDA$ . Prove that $\angle MAB = \angle MCB$. Source: Romanian Mathematical Gazette no. 5/2023
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### How to determine the reflex angles in a concave polygon in 3D?

For a concave polygon in 2D, it's easy to use the cross product to determine the reflex angles, which are greater than $180^{\circ}$, but I wonder if there is a simple way to do it in 3D.
1 vote
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### Definition of Angle between Complex Vectors

According to Wikipedia, the angle between two complex vectors $u$ and $v$ in the Vector Space $\mathbb C^n$ over $\mathbb C$ is given by \theta=\cos^{-1}\left(\frac{\operatorname{Re}(u\cdot v)}{\|u\|...
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### Why do complex numbers lend themselves to rotation?

In the introductory complex analysis course I am taking, nearly every theorem relates to rotation and argument. Why do complex numbers love doing this so much? I can understand why these theorems work;...
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### How many angles are being formed in the attached image?

Could anyone help me understand the answer of this question? This question is asked in 6th grade as part of the CBSE curriculum. I think the answer should be 4 due to 4 right angles. Should the 4 ...
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### Construction of parallel lengths in given ratio

An angle is given and two points $M$ and $N$ inside it. Through these two points, draw parallel lines $m$ and $n$ so that lengths formed by their intersections with the angle arms are in ratio 1:3. ...
1 vote
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### Prove that $CR$ bisects $\angle C$

The external bisector of $\angle A$ of triangle $ABC$ meets $BC$ produced at L and the internal bisector of $\angle B$ meets $CA$ at $M$ if $LM$ meets $AB$ at $R$ prove that $CR$ bisects angle $C$. ...
1 vote
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### General form of an ellipse - where does this error come when calculating $\theta$?

The « Ellipse » page of Widipedia, https://en.wikipedia.org/wiki/Ellipse, gives a lot of formulas in paragraph General ellipse, to switch between canonical form ...
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### How to calculate the solid angle of a rectangle?

Let $R$ be a rectangle with vertices $\boldsymbol{n}_1$, $\boldsymbol{n}_2$, $\boldsymbol{n}_3$ and $\boldsymbol{n}_4 \in \mathbb{R}^3$. I am looking for a formula for calculating the solid angle ...
27 views

### Meaning of symbolic representation of angle between two lines $\angle (\ell_1,\ell_2)$

So I was writing a solution to a problem, and I noticed that it would be unnecessary to add the point of intersection between two lines (say $\ell_1$ and $\ell_2$) to just represent the angle formed ...
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### If $\gamma$ is a smooth closed curve around the origin in $\mathbb{C}$, then $\arg\circ\gamma$ is differentiable almost everywhere

Let $\arg\colon\mathbb{C}\setminus\{0\}\to(-\pi,\pi]$ be the argument function. Suppose that $\gamma\colon[a,b]\to\mathbb{C}$ is a smooth closed (i.e. $\gamma(a)=\gamma(b)$) curve around the origin. ...
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### Why square side from its diagonal does not equal $\frac{\sqrt{2}}{2}$?

If diagonal of square is known, we can consider the square as two triangles. We know hypotenuse of the triangles and all of angles ($45^\circ$, $45^\circ$, $90^\circ$). So, as in picture above, if we ...