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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825 views

N-Dimensional “Angles” Between Vectors [closed]

So I'm wondering if there is an elegant means of displaying an angle in higher dimensions. Fair warning, I'm not sure if I'm explaining myself very well here, but I shall attempt to do so as best I ...
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1answer
117 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 ...
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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^...
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1answer
536 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 ...
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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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2answers
588 views

Finding the solid angle subtended at a viewer's eyes by a movie screen

I've got to calculate which is the seating row of a movie theater which has the greatest angle of vision. To calculate this, I would like to consider the movie screen as having two dimensions (length ...
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0answers
76 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 ...
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1answer
99 views

Is the angle of a line from the bottom-right to the top-left of a graph always $45$ degrees? [closed]

I have a theory. Let's say we have a graph, and a line from the bottom-right to top-left \ \ \ y \ \ \ \ x axis Knowing that a straight ...
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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 ...
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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 ...
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3answers
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Loops when drawing constantly changing angles and lines. [closed]

I start by drawing a line of 1 unit on the $x$ axis. I turn left (from the perspective of an ant on the line) by an angle of $\alpha$ and I draw a second segment of length $u$ from my endpoint of the ...
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3answers
164 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: $$\...
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5answers
1k views

what is the value of angle A

The triangle ABC is random. The line $AD$ is twice big as the line $DC$ ($AD=2*DC$). We know only the two angles that are shown in the picture. What's the value of angle $A$?
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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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2answers
130 views

What's the closest anyone has got to trisecting an angle with compass and straghtedge?

I know it's not possible to perfectly, trisect an angle with compass and straightedge, but what's the closest anyone has gotten to doing this?
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1answer
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New Maths 9-1 GCSE for 2017 Sample Question

My teacher gave me some practice questions for my end of year exam which will be like the new GCSE and this question is very tackling to me. Could any with clear working solve the question and show me ...
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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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89 views

Inscribed trapezoids problem

Let $ABCD$ be inscribed trapezoid with $(AB) \parallel (CD)$ and let $P$ be the point where its diagonals meet. The circumcircle of $\triangle APB$ meets line $(BC)$ (again) at $X$. $Y$ is a point ...
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2answers
56 views

Find an angle not on the circumference of a circle problem. [closed]

I know this has to be extremely easy but I'm not going to solve this problem. The task is to find the angle at point $A$. Thanks!
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2answers
74 views

Finding the location of point P

Is it possible to find the location of point $P$ such that the angles $\theta_1=\theta_2$ or $\alpha_1=\alpha_2$? I know only the locations of $O$, $C_1$, and $C_2$.
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2answers
510 views

Find the measure of ∠PRQ, with points $P(0, 3, 0) \;\;\; Q(-3, 4, 2) \;\;\; R(-2, 9, 1) \;$

I'm trying to solve the problem in the title but I'm having loads of trouble doing so. I'm not sure what angle the question is asking for. Even if I did, I'm not completely sure how to go about it. ...
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2answers
76 views

How can we determine the point at which the distance between vectors is equal to a certain constant?

Consider the following points: $$A(-3,0)\hspace{1cm} B(3,0)\hspace{1cm} C(x,y)$$ Now consider the following vectors: $$CA\hspace{1cm} CB\hspace{1cm} CO$$ where $O$ is the origin $O(0,0)$. Consider ...
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3answers
158 views

arctan and arcsin equation

How can I prove that : $2 \arctan(x) + \arcsin \Big( \frac{ 2x }{ 1 + x^2 }\Big) = \pi$ , $x > 1$ What is the best way to do this ?
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4answers
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Do Zero degree angles exist?

If an angle is the measure of distance between to points (Edit: Ok, admittedly bad phrasing. A measure of rotation between two intersecting lines, or points, etc.), is there such a thing as a zero ...
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2answers
123 views

Geometry - Find angle ∠C of a triangle given angle bisector and two segment ratios. [closed]

In the triangle ABC, one has $∠A = 70^o$. The point $D$ is chosen on the segment $AC$ such that the angle bisector $AE$ intersects the segment $BD$ at the point $H$, with the following ratios $$\...
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2answers
48 views

How is this angle measured in the triangle?

I am reading George Polya's "How to Solve It". I cannot understand how he is getting to certain solutions. Like the one from the chapter of "Auxiliary Solution". Given the image below: Let the angle ...
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2answers
214 views

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
739 views

How to derive sides for 30-60-90 triangle? [closed]

I first convert everything to radians about a unit circle. $\frac{\pi}{6}$ angle from the center, $\frac\pi2$ right angle, $\frac\pi3$ angle remains. Hypotenuse is 1. How do I figure the ratios so I ...
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3answers
121 views

a problem with condition $\sin(2\theta) = \tan(\theta) - \cos(2\theta)$

If $\theta$ represents an angle such that $\sin(2\theta) = \tan(\theta) - \cos(2\theta)$, then $\sin(\theta) - \cos(\theta)=$...? I've been trying to do this problem for a while, but for some reason, ...
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3answers
76 views

Find angle given ratio between sine and angle

I know an angle is between 0 and $\pi$ (180 degrees). I know the ratio between its sine and the angle itself. Specifically it's $\frac{15}{16}$, but I am more interested in the general case. Since ...
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3answers
1k views

Angles between lateral faces of any rectangular-based pyramid

I was just wondering if anyone had any idea how to solve this problem: What is the angle between lateral faces of a rectangular-based pyramid with length a, width b, and height h, in terms of a, b ...
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2answers
170 views

Parallelogram and Congruence

Let point M be outside the parallelogram ABCD such that $\angle MAB = \angle MCB$. Prove that $\angle AMD = \angle CMB$. I am trying to prove $\triangle MDE \sim \triangle MBC$ but I am having ...
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3answers
2k views

When do you take into account the +2kpi for complex numbers arguments in complex equations

$$z^2 = ({2e^{i{\frac{\pi}{3}}}})^8$$ To find z I took the square root of both sides which gives me: $$z = ({2e^{i{\frac{\pi}{3}}}})^4$$ which I rewrote as $$z = {2^4e^{i{\frac{4\pi}{3}}+2k\pi}}$$ ...
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1answer
110 views

Show that $\angle$AXC = $\angle$ACB

The image shows an acute angled triangle of 30 degrees with sides of 8cm & 5 cm. A perpendicular has been constructed from point A to the side BC. & the point it meets side BC is marked D. A ...
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5answers
129 views

Is the substitution of standard angles while proving the equality of trigonometric formulas allowed?

Here is a problem that my class 10 maths teacher gave me: Prove that $\sec^4\theta$ - $\sec^2\theta$ = $\tan^4\theta$ + $\tan^2\theta$ She expected me to use trigonometric identities to prove such ...
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1answer
35 views

Calculate angles of a polygonal shape given by its sidelengths

Can someone tell me how to calculate the angles of this shape. The length of all sides are given. I need to say that these are just example side lengths ; I need a formula for variable lengths.
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3answers
62 views

Inside a circle: Four triangles with equal area, 5 unknown angles

In this circle, I have four triangles equal area: $$A_1=A_2=A_3=A_4$$ and 5 unknown angles.Is it possible to find the value these angles? Given $$\alpha=?$$ $$\beta=?$$ $$\gamma=?$$ $$\...
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1answer
64 views

If the number of degrees in certain angle is added to the number of grades the angle is $152$, find the angle in degrees.

If the number of degrees in certain angle is added to the number of grades the angle is $152$, find the angle in degrees. My Attempt Let $x$ be the angle. Then no of degrees in $x$ is $\dfrac {10x}{9}...
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1answer
40 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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2answers
169 views

Angle trisection of $90^o$

Read on page #7 of article here, that angle of $90^o$ can be trisected. I went through this youtube video here, and here; and denote these two videos (denoting two separate methods) by (a), (b) ...
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3answers
74 views

How to draw a line of intersection of a line at an angle?

I have a line called $AB$ with the points $A (40, 40)$ and $B (280, 40)$. I have an angle $D\simeq 48^\circ$. I want to draw a line $CE$ from the center of the line $AB$, which is $C (160, 40)$ with ...
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1answer
63 views

[High School]How to find out the other two equations?

I have been trying to solve this question The question asks to prove that- $α=β=γ=30$. I am trying to solve this question by discovering equations. Since,we need to find out the values of three ...
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2answers
50 views

Can a secant-secant angle ever be obtuse?

If two secants to a circle are drawn from the same exterior point, can the angle formed between the 2 secants ever be obtuse (or right)? Thank you
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1answer
345 views

How do I find the angle of intersecting circles?

I'm a software engineer not a mathematician so I apologize if I'm not using proper language or if this was answered before (I couldn't find it). I have two circles. I know the positions and radius of ...
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2answers
2k views

Length of two sides in a quadrilateral with given angles

I'm stuck finding the length of two sides in a quadrilateral for which I know all angles and the length of two sides. All red objects are know ($a,b,\alpha,\beta,\gamma $ and $\delta$). I need to ...
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2answers
748 views

Interpolating Between 2 Angles

I'm trying to understand how this works, and mathematically I'm having difficulty. Given 2 angles between $(-2\pi, 2\pi)$: $\theta$ and $\phi$ I want to interpolate between them by the ratio: r. My ...
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2answers
78 views

Find the angle between vectors [closed]

Parallelogram constructed on the vectors $a=5p-2q$, $b=3p+2q$, $|p|=2$, $|q|=3$, $(p\wedge q)=120^{\circ}$. $\sin(a\wedge b)=???$
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2answers
5k views

Finding subtended angle at the centre of a circle from known arc length

I have the question "What angle is subtended at the center of a circle of radius $2$ km by an arc of length $9$ m?" I am not sure which formula to use to find the subtended angle.
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2answers
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How to get the angle between polar coordinates without converting to cartesian

I'm trying to work out a way to get the angle between two points given in polar coordinates, without first converting them to x,y. I (sort of) remember enough high school trig to do it with x,y but I'...
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1answer
70 views

Pythagorean triplet mutiple angles

If both cos and sin are rational, then, is sin(nx) rational? From just checking for obvious values other than, 0,1 For tan(x)=3/4, for n=2, we get another pythagorean triplet of 24,7,25, for n=3, ...