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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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34 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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46 views

Is this question valid? If $\angle A$ and $\angle B$ are complements, and the supplement of $\angle B$ is $78^\circ$, then find $\angle A$.

Question: Angle A and B are complementary. If the supplement of angle B is 78°. What is the measure of angle A? I am confused since A + B = 90 B + 78 = 180 B = 102 A + 102 = 90 A = -12 I think the ...
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1answer
21 views

Calculating angle made with center of room - am I doing this correctly ? What method can I use?

The room Note: it is say supposed to say 4,0 for the first location. 4,4 refers to the center of the room. Basically I have cameras placed in those three locations - (4,0), (0,8), and (8,8). I want ...
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0answers
14 views

How to get the angle between the bisector (with 3 points given) and the abscisse.

I have three random points in a 2D space, $A$, $B$ and $C$, how can I compute the angle between the abscisse and the bisector of $ABC$: So I am looking for the angle $α$ (in red). I'm using a ...
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1answer
26 views

How can I find the angle of the surface/3D Plane.

I have a plane with equation 3x + 2y + 5z - 19 = 0. With the help of Python/MatPlotlib, I could draw this plane also. Please find the image below. What I would like to know is how to determine the ...
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23 views

How an N dimensional rotation matrix can be constructed with more than one degree of freedom

Say we have a point or a line in a three dimensional space, which we can rotate it around the origin by two angles, one with respect to axis 1 and the other with axis 2 or 3 (two angles(degrees of ...
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1answer
35 views

How to find an angle between the extension of a diameter and a chord in a semicircle

O is the center of the semicircle, if $\angle EOD = 45^\circ$ and OD = AB, find $\angle BAC$ I don't know what theorem I should use, I've tried to connect many dots to reach the answer but still can'...
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1answer
33 views

i cant find $\tan\theta$ i think i need to use ratios or similarity some how

if you can help me with finding $\tan(\theta)$ it would help me a lot, as I wanna know how to do it and what identities to use, possibly triangle similarities or something to do with ratios question #...
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1answer
27 views

Parallelogram OPQR is such that OP=[-7,24] and OR=[-8,-1] determine the acute angle between the diagonals OQ and RP.

I'm just really stuck on this question I only found the magnitude of OP = 25 and RP=√65
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2answers
53 views

Why is there an angle of $\frac{\pi}{6}$, and not $\frac{\pi}{2}$, in this problem?

I struggle with the following explanation, and would be grateful if you could help. Thank You. "Consider a small hole with area $a$ on the surface of the metal cube through which radiation can escape....
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4answers
70 views

How to prove $\vec{a} \perp \vec{b}$ when $|\vec{a}-\vec{b}|=|\vec{a}+\vec{b}|$? [duplicate]

I have tried to show that $cos(\theta)=0$ by substituting what is given into $(\vec{a}-\vec{b})\cdot(\vec{a}+\vec{b})=|\vec{a}-\vec{b}||\vec{a}+\vec{b}|cos(\theta)$ but after simplifying i get stuck ...
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0answers
55 views

Product of sines to sum

I stumbled across the following identity in a system I'm considering: \begin{align} \prod_{j=1}^N \sin a_j \end{align} which I need to rewrite as a sum (or otherwise) of sines or other expressions. $...
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2answers
54 views

How to determine whether a triangle is obtuse angled or not from the equation of its sides?

Suppose we are given the equation of the sides of a triangle, how can we determine whether the triangle is obtuse angled or acute angled? In case of a right angled triangle, I would simply check ...
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1answer
24 views

How to find the angles of a trapezoid

The perimeter of a trapezoid is 5 and the lengths of its sides are integers. What are the smallest two angles of the trapezoid. The perimeter is 5 so I get 1*2+1*1+2*1 as the sides. But how do I ...
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41 views

Simple Geometry: Best angle to view trees from fixed camera

I am trying to solve this question: Given a fixed camera in a forest (with predefined trees), give the best angle in which the camera pictures the maximum of trees. The solution I have come up ...
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1answer
21 views

Existence of Right Angle in Hilbert Axioms

Hilbert, in Foundations of Geometry briefly mentions that the existence of right angles is a corollary to the supplementary angle theorem. (i.e. If two angles are congruent, then their supplementary ...
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53 views

Proving a formula in geometry

I've the following diagram given: The two main lines are parallel. Theorem: $$\left|\text{GG}'\right|=\left|\text{KM}\right|\sin\varphi-\left|\text{KG}\right|\sin\varphi=\left|\text{GM}\right|...
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1answer
54 views

Angle bewteen two vectors

I have encountered such problem that ask us to calculate the angle between two vectors: $\vec{u},\vec{v},\vec{w}$ has a length of $5$,$12$,$15$ respectively. Their sum gives a $\vec{0}$. What is ...
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29 views

Mirroring an angle over the Y axis

This question is a follow-on from this one posted on Stack Overflow. I'm working with an application that uses a function to calculate the points on an arc given the following information: Start ...
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1answer
21 views

How to find height of a building from its changing shadow?

The shadow of a building increased by 10 meters when the angle of elevation of the sun decreased by 10 degrees from 70 degrees to 60 degrees. Calculate the height of the building. I tried to ...
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0answers
23 views

Angle between two vectors: 3D No magnitudes and/or sqrt()

Hey so I have a very efficient method to calculate the the components (x,y,z) of two vectors, and I want to calculate the angle between them. I am computing this for about 8 million individual entries....
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1answer
25 views

Prove that all the inscribed angles are equal

Consider a circunference that contains 3 inscribed angles which are opposite to the same arc Prove that all the angles are equal. (See image for detail) https://i.stack.imgur.com/5Wz3Y.png
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Finding an interior angle between two interior angles

In the picture below; shows how it is illustrated: https://imgur.com/a/2DVsM4x I am trying to find angle b; given angles a and c. The value for angle a is 32 degrees, and for c it is 77degrees. How ...
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1answer
60 views

Ratio of areas of triangles

There's this geometry problem I tried to solve, but I am not sure if my solution is the easiest one. First I'll explain the problem: Let's say we have a triangle ABC, a point X in the third of side ...
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0answers
17 views

How to add 42 degrees to either the X/Y/Z axis in quaternions

The picture below is showing a human bone. Red is the bone/object (humerus bone/the bone on your bicep) Orange is X axis Purple is Y axis Pink is Z axis Link to image If the current rotation of the ...
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2answers
27 views

Measure angle between two segments with one shared point

I have given points $A(x_1,y_1);B(x_2,y_2);C(x_3,y_3)$. I have two segments $CB; AB$. I need to measure angle $\alpha$, located between segments $AB$ and $CB$. Is there a formula to calculate angle $\...
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0answers
15 views

Angles between normal vectors vs angles between faces

I am to prove two different formulas, but I don't get how are the values in the formulas different. This is a tetrahedron problem, specifically angles. At first, I am supposed to prove $\ A^2 = B^...
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1answer
62 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}{...
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0answers
13 views

Can the projection of two vectors be used to approximate the angle between them?

I am supposed to use a secondary justification (other than using the inverse cosine of the dot product divided by magnitude) that the angle between two vectors (117.429 degrees) is obtuse. The two ...
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1answer
48 views

Virtual rolling contact joint

It started with this video: https://youtu.be/aLaqMreVj9o?t=56 showing a "Virtual Rolling Contact Joint" - VRCJ: and then pmesten18 made a model in Fusion 360 here: https://forums.autodesk.com/t5/...
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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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2answers
41 views

Finding side length from two scalene triangles with common angle and side and ratio between sides. Trigonometry

I have two scalene triangles with a common angle and side. I would like to find the length of $x_2$. I have all variables in green: the angles $\angle$ B,$\angle$ C,$\angle$ D,$\angle$ E and side "...
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2answers
43 views

Knowing $\sin(45^\circ)={\sqrt2\over2}$, how do I find $\sin(135^\circ)$ and $\cos(135^\circ)$?

I just know about $$\sin(45^\circ)={\sqrt2\over2}$$ and I want understand how to find $\sin(135^\circ)$ and $\cos(135^\circ)$ Thank you.
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1answer
21 views

The angle between a segment and the OX axis given segment origin, length and a perpendicular segment

Given a point $A(x, y)$ in a $2$D plane and two perpendicular vectors having their origin in $A$ with their corresponding magnitude (length). Also given that the $2$ vectors are perpendicular, is it ...
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2answers
39 views

reverse proof of sin30 = 1/2 without trigonometry

The length of one side of the right triangle (AB) in the picture is half of the length of the hypotenuse (AC). How can I prove that $\angle ACB = 30^0$ , without using trigonometry?
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0answers
30 views

Math formula for Real life distance to phone screen adjustment

Please help me! The picture below will give some depiction of what i'm creating. I'm trying to create a smartphone application for straight road construction control. The idea is to let this app ...
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1answer
25 views

Angles and rates of change

I'm trying to get my head around the following problem, any help is appreciated. My maths skills aren't the best, so apologies in advanced for its stupidity. Say I'm in a car, and I'm driving ...
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1answer
32 views

Going From a Matrix to Eulers When Cosine is 0

Given a rotation matrix created from the Eulers $\phi$, $\theta$, $\psi$ like this which I want to take back to Eulers: $$ \begin{bmatrix} \cos\theta\cos\psi & -\cos\theta\sin\psi & \sin\...
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2answers
46 views

Is would possible to describe length just in degrees

In 2d space I have two cameras with different field of view ($40$ and $46$ degrees in my example) and have some distance between them. Is would possible to describe this distance using just this two ...
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0answers
37 views

Geometry problem regarding an isosceles triangle [duplicate]

Consider the following isosceles triangle (not drawn to scale) where $\alpha=70^\circ$, $\beta=10^\circ$, $\gamma=20^\circ$ and $\delta=60^\circ$. Find $x$. A friend ...
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3answers
61 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 ...
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0answers
29 views

Wrapping around a vertical facing angle

$a$ is a vertical facing angle in 3D space, it can be from -90 to 90. I need to add $b$ to it and have it result in a vertical angle "wrapped" around to the other side with the horizontal angle facing ...
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2answers
121 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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1answer
69 views

Help! In quadrilateral $ABCD$, angle $BAD$ and angle $CDA$ are trisected as shown. What is the degree measure of angle $AFD$? [closed]

Help! I have a math problem that's been confusing me a lot. Source: AoPS Staff The problem is: In quadrilateral $ABCD$, angle $BAD$ and angle $CDA$ are trisected as shown. What >is the degree ...
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1answer
50 views

Proving another point lies on a circle

Five congruent circles, with centres C, D, F, G and H, are arranged so that each centre lies on the circumference of at least two other circles, as shown in the attachment below. a) Let P be the ...
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3answers
47 views

How to calculate angle bisectors and intersection points of them for a polygon to construct straight skeleton?

I am trying to construct staright skeleton of a polygon. I have coordinates array of polygon. How to construct angle bisectors of lines using coordinates? And then how can I calculate intersection ...
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1answer
49 views

Transformation that do not modify angles

How can I prove for $R_2$ that the matrix $$T = \begin{bmatrix} a & b \\c & d \end{bmatrix} =\begin{bmatrix} a & b \\-b & a \end{bmatrix} $$ is the ony one that, when multiplied with 2 ...
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2answers
50 views

How to calculate angle bisector of 2 lines using x, y coordinates in 2D and intersection point of angle bisector directions

I have lines which are represented with start and end coordinates. These lines are edges of a polygon .For example, Line 1 is represented as (x1,y1), (x2y2) and Line 2 represented as (x3,y3), (x4,y4). ...
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1answer
23 views

Is it possible to determine how far into a wedge of a known angle you can place a circle of known dimensions?

Apologies for the title, I found it hard to express this succinctly in words alone! Consider the following image, where A is a known angle (<=180°) and <...
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2answers
112 views

Find $\angle CAD$ in following figure.

In $\triangle ABC$, $\angle ACB =20°$ and $\angle CAB = \angle CBA=80°$ $D$ is a point on $CB$ such that $CD=AB$ Find $\angle CAD$ I assumed $\angle CAD=\theta$ and $AB=CD=x$ Applying sine ...