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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).

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Field of view angle taken up by a sphere of a certain radius at a certain disance [on hold]

Is tan(radius/distance) the correct way to work out the angle of the two grey lines in this diagram? Thanks for the help.
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1answer
39 views

How can I solve x in this shape?

I've been learning angles on lines and in shapes but I've been struggling with how to go about solving this. Usually you're given more angle values or at least a side value as a starting point - ...
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0answers
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Proving plane geometry problem

Given 8 lines on a plane and no two of them are parallel. Prove that, at least two of them form an angle less than 23°. I have checked this out using different angles and the statement seems to be ...
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1answer
21 views

Phasor/Harmonic Addition Formula/Theorem: Why can we take out the frequency out of an complex argument?

Harmonic Addition Theorem Harmonic Addition Formula Phasor Addition Theorem Phasor Addition Formula Those four name can be used as a keyword on google. I haven't known the official name and think ...
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0answers
27 views

Need help on a problem on trigonometry

In triangle ABC, AB=10, CA=12. The bisector of ∠𝐁 intersects CA at E, and the bisector of ∠𝐂 intersects AB at D. AM and AN are the perpendiculars to CD and BE respectively. If MN=4, then find BC. ...
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1answer
36 views

Need help on a trigonometry problem

The question is- Points D and E divide equal sides AC and AB of an equilateral triangle ABC according to the ratio of 𝑨𝑫: 𝑫𝑪 = 𝑩𝑬: 𝑬𝑨 = 𝟏: 𝟐. Edges BD and CE meet at point O. Find ∠𝐀𝐎𝐂. ...
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0answers
16 views

Move a point in 3D space a given distance and angle

so I'm fairly new to maths and need to know how to move a given 3D point in space, a certian distance and a certian angle and get the new position, that angle being in radians and being an x angle and ...
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1answer
15 views

Angle required to rotate a polygon towards the direction of a vector

I have a problem where I need to rotate a polygon so it has the same direction as the vector $v_1$ (the pointy head face $y$-axis +ve). I tried a solution where I take two vectors one the $y$-axis: ...
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1answer
28 views

Angle created by three distincts random vertices

Assume you have a regular polygon ( $n$-sides). and Let $A=\{ x_0, x_2, \cdots , x_{n-1} \}$ be vertices of the polygon. My Question is: Are there is any formula that tell us what is the angle ...
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2answers
39 views

To find the bisector containing the point

Given two Non Perpendicular lines $3x-4y+1=0$ and $12x+5y-3=0$ Find the equation of bisector containing the point $(1,2)$ My try: Using the formula for angle bisectors we have: $$\frac{3x-4y+1}{5}=...
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0answers
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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 ...
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1answer
28 views

How do i calculate the angle $\theta_L$?

I need to find the angle $\theta_L$ in the attached sketch. The variables I know are: $R_L$, $R_G$, and $\theta_G$. So i need a formula for $\theta_L$ in terms of these. $R_g$ is also the distance ...
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1answer
30 views

What is the length of the arc on the unit circle subtended by an angle of 120 degrees? Show all work.

What is the length of the arc on the unit circle subtended by an angle of 120 degrees? Show all work. 2/3 1/3(pi) 2/3(pi) pi I used an equation where the central angle equals the arc length divided ...
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3answers
61 views

Prove that AM is perpendicular to BD [duplicate]

In the isosceles triangle $ABC$, $M$ is the median of $HD$ and $AH$ is perpendicular to $BC$ and $HD$ is perpendicular to $AC$. Prove that $BD$ is perpendicular to $AM$.
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1answer
63 views

3D rotation defining the intersection of 2 planes

Triangles $DAE$, $DCE$ and $DBE$ form a quadrangle $ABCD$, where $\angle BAD$ and $\angle BCD$ are right angles. I have a scenario in which I want to find the angles $\angle ABD$ and $\angle DBE$, ...
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1answer
21 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 ...
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1answer
26 views

Making a formula that finds the horizontal and vertical distance between two points that change with a new angle.

I am making a Scratch 3.0 game. The shooter sprite is holding a gun slightly off-centre (see images), and I need the bullet to go to the end of the barrel of the gun before travelling forward (as so ...
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2answers
50 views

For which $\alpha$ will take the cake ever be again with chocolate on the bottom and cream on the top

Question: A bored kid left alone at home decides to take a chocolate cream cake (chocolate on the bottom, cream on top) and his protractor and spend the day as follows: He cuts a slice of angle $\...
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2answers
29 views

Why is the angle between vectors restricted?

Why is the calculated angle between two vectors always between $\pi$ and $0$. Is this due to the limitations of $\arccos\theta$ or is it because angles between vectors is described to be the smaller ...
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1answer
51 views

Geometry triangle inside circle [closed]

Triangle $\triangle ABC$ is inscribed in a circle. $D$ is a point on $AC$. $BD$ is angle bisector of $\angle B$. $O$ is the center of the circle then find $\angle ADO$ if $\angle A=20°$ and $AB=AC.$
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0answers
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Signed angle between higher-dimensional oriented vectors?

I am working with vectors in $\mathbb{R}^4$. Any two such (non-parallel) vectors obviously define a plane, and I can rotate any vector in the plane defined by itself and a second vector as follows: $...
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2answers
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How many equally spaced points are needed around a circle of radius r such that every point is d units apart from eachother?

This question is a bit different than what I have seen here. I know how to calculate the positions such that n points will be equally spaced around a circle however ...
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0answers
33 views

Calculating the missing angle

I have the following problem where I need to find out the missing the angle. I have to apply some triangulation method to solve. I have the values of the hypotenuse. My solution is to break this ...
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2answers
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How can I find the sum of the angle $AMB$, angle $ANB$ and the angle $ACB$? [closed]

How can I find the sum of the $\angle AMB, \angle ANB$ and the $\angle ACB$? In triangle $ABC$, $\angle ABC =90^\circ$. $BC$ is divided in $3$ parts such that $BM=BN=NC$. And also $AB=BM$. Here are 2 ...
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1answer
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Apply pitch/roll measurements to different reference frame

My problem is identical to this unanswered question. IMU orientation reference image I have an IMU mounted on an object at an angle offset with that object's pitch and roll axes. When I get pitch ...
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3answers
32 views

angle and coordinator calculate from two points forming a line

Two points are given: $A (x_1, y_1)$ and $B (x_2, y_2)$. These points form a line. At point $B$ is the end of the line. I need to calculate the angle that is shown in the figure and also the ...
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0answers
21 views

If angles can be vertical, can they be horizontal or slanted?

IMPORTANT: The angles are named vertex-point on leg-point on leg. Angles are vertical if they share a vertex. $\angle ABC$, $\angle ACD$, $\angle ADE$ and $\angle AEC$ are vertical. Angles are ...
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1answer
60 views

What is it called when you subtract multiples of 360 degrees?

When you divide a vector by its magnitude to get a unit vector, there's a verb for that: you are "normalizing" the vector. Similarly, is there a verb for when you subtract multiples of $360$ ...
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2answers
41 views

Calculate arc central angle given the center, radius, start and end points of the arc

How can I calculate the angle at the center of an arc knowing radius and center, start, and end points? I know how to do that if I have the length of the arc, but in my case I don't have it.
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1answer
44 views

I want to find $\angle BAD$. [closed]

$ \angle BDC = 120°$, $\angle BEC = 160°$. I want to find $\angle BAD$.
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1answer
19 views

Conversion between angle with axis & angle with axial plane

Let's imagine in 3D space I have three angle, $\theta_x$,$\theta_y$,$\theta_z$ respectively with X-axis, Y-axis, Z-axis. Just like $\alpha,\beta,\gamma$ here: I also have $\theta_{xy},\theta_{yz},\...
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0answers
21 views

pass Euler angles from a coordinates system to another

I have a coordinates system $(\vec{x},\vec{y},\vec{z})$. In wich there is three known perpendicular vectors of length 1 that define another coordinate system: $(\vec{x'},\vec{y'},\vec{z'})$. ...
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0answers
16 views

Distance between two points at same angle in trochoid curve

Anyone please help me to find out the distance in following case. Refer to the attached image. Consider an arbitrary point P on the circumference of a circle of radius r (mm). The point makes an ...
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0answers
72 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 ...
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1answer
39 views

Average direction between two vectors

this is my first time asking a question so I'm sorry in advance for any mistake I might make. So I have 3 points in 3D space: A, B and C. What I want to do is have an object on point B point towards ...
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2answers
56 views

A problem with tetrahedron [closed]

Let ABCD be a tetrahedron with the property that opposite edges are equal. We know that the angle between the planes ABD and BCD is $90^\circ$ and the angle between (BCD) and (CAD) is $60^\circ$. ...
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1answer
29 views

Mathematical proof regarding angle mirroring

I'm trying to find a proof for a statement that is made in Griffiths' Introduction to Electrodynamics. It can be stated as follows (in my own words): Let $P$ be a point such that its angle in polar ...
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0answers
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Is there a conformal mapping from the surface of a cube to the surface of a spherical cube that preserves edges?

Is there a conformal mapping (with certain singularities noted below) from the surface of a cube to the surface of a spherical cube that preserves edges? Note that this also implies that vertices and ...
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1answer
76 views

Angle of a Star Inscribed in a Circle

I don't even know where to start on this: In the figure, point O is the center of the circle, points A, B, C, D and E all lie on the circle, and both segment AD and CE go through point O. Angle BEC ...
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0answers
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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 $\mathbb{P}V$, ...
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1answer
16 views

Does a Bijective Commutative transformation on a vector of angles exist?

I have a problem where I have two vectors a and b representing a list of angles. I need to find a transformation T where T(a,b) = T(b,a), where T has a distance metric to compare two transformations,...
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1answer
83 views

Proposition 3.14: Geometry

Please help prove the following proposition: Proposition 3.14 Supplementary angles of congruent angles are congruent. Is this right? (1) Suppose angle ABC is congruent to angle DEF (given) (2) We ...
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2answers
35 views

How to solve this equation using the cosine rule [closed]

How do you do this question using the cosine rule? A triangle $ABC$ has the following lengths: $AB = x$ cm $AC = (x+6)$ cm $BC = (x+4)$ cm $\angle CAB = 60^\circ$ Find the ...
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2answers
45 views

Triangle Geometry question find minumum value of $n-m$

In the triangle shown, for $\angle A$ to be the largest angle of the triangle, it must be that $m<x<n$. What is the least possible value of $n-m$, expressed as a common fraction? I found that $...
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1answer
54 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 ...
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1answer
20 views

Coordinates of line in sphere with x,y rotation

Lets say that I have a line with one end fixed to the center of a sphere, and the other end can freely rotate. If I were to rotate the line around the x and y axes, what would the coordinates be for ...
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2answers
45 views

Triangle problem, $AC=3$ , $AB=5$ ,…, then $PH=?$

In $\triangle ABC$ : $AC=3$ , $AB=5$ , $\angle ACB= 90 ^ \circ$, $P$ is a point inside $\triangle ABC$ such that $PA+BC=PB+AC=PC+AB$, $H$ is a point on the line $AB$ such that $\angle PHB=90^\circ$ ...
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1answer
30 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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1answer
76 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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1answer
50 views

Maximizing a pool's length

A math project I am doing asks the following: Blammo is to be fired at ground level with a muzzle velocity of $35$ m/s over a flaming wall that is $15$ m high and a ground level shark pool. The pool ...