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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).

247 questions with no upvoted or accepted answers
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6
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1answer
76 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 ...
5
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1answer
1k views

Help calculating angles for woodworking

I am working on a wood working project and need to cut some 2 x 2's on an angle in order to form an X inscribed inside a rectangle. Visually here is what I am trying to create: So basically I want to ...
5
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0answers
76 views

Dynamics of Triangle Iterates by angle bisector

I'm attempting to prove what is demonstrated in this Wolfram demo Let $T_0$ be an arbitrary triangle with vertices $A_0,B_0$and $C_0$,and let $T_1$ be the triangle formed by the intersection points ...
4
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0answers
83 views

Is it possible to prove the derivative of sine geometrically without arc length?

There are a great many ways to prove that the derivative of sine is cosine, some of them based on things like the Taylor series definition. I’d like to prove it using only the right-triangle ...
4
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0answers
84 views

What is the spherical equivalent of splitting a circle into n equal segments and calculating their central angles?

So this is easy to calculate in 2 dimensions, if you have a circle represented by 3 points the angle between any two consecutive points and the spheres centre is simply $\frac{2\pi}{n}$. I basically ...
4
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0answers
336 views

How to find rotated top, left of a rectangle given I have top, left and rotation angle

I think this is a simple problem but my Math/Geometry skills are not very good. I am given the top,left coordinates and the height & width of a rectangle as ...
4
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1answer
153 views

Bounding angles in Riemannian triangles with bounded sides

Is it true that angles in Riemannian triangles with bounded sides are uniformly bounded? More precisely, let $M$ be a Riemannian manifold. Given $0<r <s$, is there a number $\delta$ (...
3
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0answers
44 views

Prove this formula for the $\sin\left(\frac{x}{2^n}\right), x \in [0,\frac{\pi}{2}[, n \in \Bbb{N}$

The formula in question: $$\sin\left(\frac{x}{2^n}\right) = \sqrt{a_1-\sqrt{a_2+\sqrt{a_3+\sqrt{a_4+\dots+\sqrt{a_{n-1}+\sqrt{\frac{a_{n-1}}{2}\left(1-\sin^2(x)\right)}}}}}}$$ where $$a_k = \frac{1}{...
3
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2answers
104 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 ...
3
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0answers
53 views

How can we calculate the sum of sines or cosines where the angles are in geometric progression?

For example: $$\cos\frac{\pi}{7} + \cos\frac{3\pi}{7} + \cos\frac{9\pi}{7}$$ In this example, there are only a few terms, and we can use things like $\cos(9\pi/7) = -\cos(2\pi/7)$ and complex ...
3
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0answers
136 views

How to find optimal solar panel angle using vectors?

Basically I am trying to find the optimum angle at which a solar panel should be installed by using vectors. I have done some research but found it a bit confusing , so basically I haven't got very ...
3
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0answers
52 views

Please explain how the following derivative graphically makes sense.

I have two vectors $\vec{A}$ and $\vec{B}$ as shown below: The point at the origin of vector $\vec{B}$ has coordinates $(x,y)$. The angle between the two vectors is $\theta$. Now in my physics book ...
3
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0answers
62 views

Formula for minimum distance for circles what won't touch each other depending on n?

Let's say that I have a circle, which is the "middle circle" (red in the pictures below). I also have a number (n) of identical circles, that should appear around the middle one, without touching. For ...
3
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1answer
191 views

Exact Dihedral angle for Disdyakis Triacontahedron

I've tried calculating the exact dihedral angle of a Disdyakis Triacontahedron, with no success. I cannot seem to find it online either. What is the correct approach to trying to figure out this value?...
3
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1answer
58 views

Proving angles in the same corner equal

Suppose we have two line segments, AB and CD, which cross at point X. Now suppose there is an arbitrary point Y somewhere on the segment AX (that is, points A, Y and X are collinear). What is the ...
2
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0answers
37 views

Phase angle of a Fourier series

I have read in my textbook that if a Fourier series consists of only sine terms(that is, the function is odd), its phase angle is 0. If the Fourier series consists of only cosine terms(that is, the ...
2
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0answers
97 views

Calculate 3d Rotation Maintaining Orientation

My Current Setup: Let's assume we have these 3 axes in 3d space. Let's also assume that x = blue; y = red; green = z; To calculate a rotation on the x axis, i.e.,...
2
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0answers
33 views

Why is it important to get the cosine of an angle theta instead of the angle itself in two unit vectors?

I'm a bit confused about why is it important to get the cosine of an angle theta instead of the angle itself in two unit vectors? I mean, to get the cousine theta angle we need to dot product of the ...
2
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0answers
37 views

Change of angle inside a quirky hexagon

So I am dealing with the hexagon as shown in the picture below and I need to find out how one angle depends on another angle. More specifically, I need $\frac{d\psi}{d\varphi}$ at $\varphi=0$. Note ...
2
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1answer
57 views

At what angle from the ground should it be fired so that it travels the maximum distance in the air?

A projectile is going to be fired from a cannon on level ground. At what angle from the ground should it be fired so that it travels the maximum distance in the air? Details and Assumptions: There ...
2
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2answers
326 views

right angle equal to obtuse triangle?

Given the obtuse angle x, we make a quadrilateral $ABCD$ with $∠DAB = x$, and $∠ABC = 90◦$, and $AD = BC$. Say the perpendicular bisector to $DC$ meets the perpendicular bisector to $AB$ at $Q$. Then $...
2
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1answer
115 views

Finding the Point Along a Line Such that an Axis-aligned Box Around the Point Doesn't Exceed Another Line

Given two line segments $L1 = (P1, P2)$ and $L2 = (P2, P3)$, the width and height $(W, H)$ of a rectangle, and the angle between $L1$ and $L2$ $(\phi)$, how would I determine the point $Q$ on L1 such ...
2
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0answers
216 views

Find angle $\alpha$ in this triangle question.

In triangle $\triangle{ABD}$, $C\in BD$, $E\in AD$, $BE\cap AC =\{F\}$ $B,F$ and $E$ are collinear. $AB$ is the angle bisector of the $\measuredangle{HAC}$. $\measuredangle{HAB}=\measuredangle{BAC}=50^...
2
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1answer
518 views

Why do we get angle between planes by taking dot product of the normal vectors?

Let theta be the angle between 2 planes. Then to find this angle we take the dot product of the two normal vectors to the plane, divide by their magnitudes and then finally take the arccos of the ...
2
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0answers
4k views

Angles of a known 3d vector

I have a 3d vector r known by its coordinates rx, ry, rz. How can calculate angles Theta and Phi ?
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0answers
75 views

Terminology to distinguish angles spanning 180° from “oriented”/“directed” angles spanning 360°?

In some contexts it makes sense to talk about angles between vectors that can span a full 360° because there is some natural orientation. As an example, for points on the unit sphere, we can assign ...
2
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2answers
47 views

Find Length of line which has rotating object.

I have 3 Images. A, B and C. if I place it on graph, its look something like this. Now main image is A and I place B and C on that image's (A) center point. For easy understanding, let's consider ...
2
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1answer
45 views

Degree measure of circles

One slice of a circle which has been divided into 360 slices is one degree right? If this is the case, won't bigger circles have bigger slices and therefore bigger degrees? Why is one degree of a ...
2
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3answers
135 views

Is there any expression to calculate the sum of (at least) 3 cosines?

I'm envolved in a waves problem and I have to calculate $\cos(A)+\cos(B)+\cos(C)$, where $A$, $B$ and $C$ are independent angles. I want to find a expression similar to the sum-product identity: $$\...
1
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1answer
19 views

Vehicle weight on a slope?

A vehicle needs to winch in a cable with 1000lbs of pressure/weight. The vehicle weighs 5400lbs How much of a slope must the vehicle park on to achieve 1000lbs of weight to winch in the cable?
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3answers
59 views

How to find 2d angles for 3d vectors?

I have three vectors in 3d that originate at a point. If I look at them along a line perpendicular to a plane that intersects two of them, how do I find the angles between those two vectors and the ...
1
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0answers
27 views

Angle between polar curve and a tangent to a circle

Suppose I have a polar curve written as $\theta = f(R)$ where $0<f(R)<2\pi$ for all $R$. I want to find the angle between this curve at radius $R_0$ and the tangent to the circle with radius $...
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0answers
29 views

Calculate Third Point of Triangle knowing Vector

I have 3 points and their coordinates $(A, B, C)$. Then I have new coordinates of points $A'$ and $B'$ How to calculate the coordinates of point $C'$ knowing that the distance from point A to point C ...
1
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1answer
25 views

Length across cuboid at an angle

I would like to calculate the change in length across a cuboid when looking at it from different angles (e.g. 10 and 20°). In the illustration below the red arrows show the length I would like to ...
1
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0answers
37 views

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 $\mathbb{P}V$, ...
1
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1answer
272 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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0answers
48 views

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:...
1
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1answer
43 views

Height of a Triangle, and a Progression of Triangles

I am researching some algorithms and it turns out that the following figure I made can model what is happening in a "step". I am not a mathematician, so I was having a hard time with this one. The ...
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0answers
59 views

How to find change in angle when vertical Scale of depth axis is modified?

Let Q be the Quaternion that perform a rotation of angle degrees around some axis of rotation. Later I change vertical exaggeration of my Vertical axis (z) to some value VS, e.g. make the vertical (z) ...
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0answers
39 views

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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0answers
27 views

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
33 views

Find the angle of a point in relation to a 3d basis …

The question is quite hard to explain so I included a diagram, what I'm trying to do is to solve for the two angles indicated by clouds, in the quickest way possible. As for the vectors, they are 3 ...
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0answers
69 views

Angle between two lines/vectors (both magnitude and sign)

Difference in angles for 4 cases Attached figure shows small part of bigger problem. The circle of radius 5 is divided into 4 segments. Midpoints of these segments are marked (e.g. O). From the ...
1
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1answer
322 views

Distribution of angle between two dependent gaussian random vectors

Suppose that $x,y \in \mathbb{R}^n$ have i.i.d. $\mathcal{N}(0,1)$ entries. For some scalars $\alpha,\beta \in [-1,1]$, I am interested in the distribution of the angle $\theta$ between $x$ and $\...
1
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1answer
62 views

Double Angle in Circumscribed Triangle

In triangle $ABC$, angle $ACB$ is $50$ degrees, and angle $CBA$ is $70$ degrees. Let $D$ be the foot of the perpendicular from $A$ to $BC$, $O$ the center of the circle circumscribed around triangle $...
1
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1answer
22 views

How are you supposed to find n of an n-sided polygon given part of two interior angles

I need to work out the below question, but I have no idea what to do. I tried researching but the results were assuming that I know the entire interior angle And I'm not even sure if this is a polygon,...
1
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0answers
43 views

Find the smallest number of acute angles which add up to a full angle. Same with obtuse angles.

Find the smallest number of acute angles which add up to a full angle. Same with obtuse angles. I've got this problem, and I tried to solve it, but I don't know if my reasoning is correct, and formal ...
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0answers
55 views

Local coordinates and angle function

I'm stuck with this problem: "Let us consider, on the sphere, the local coordinates associated with the differential structure determined by the atlas $\{(U_1=S^n\setminus\{N\},\varphi_N),(U_2=S^n\...
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0answers
99 views

Deriving Formula for internal and external angles of a concave polygon

How to derive formula for internal and external angles of a concave polygon. The internet shows that the formula is same as a convex polygon, but how can we derive it? Thank You.
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0answers
22 views

Is there a term for angles which are coterminal with 0?

Quite simply, is there such a term, either an adjective, as in such an angle is called a [insert word here] angle or a noun as in such an angle is called a [insert word here]? Because I feel like it's ...