# 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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178 views

### Solve for the angle x?

The problem seems really impossible to me, despite solving many problems on triangles. So I hope that you can solve it. src:https://www.instagram.com/p/BtUNj3IBIW5/
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### Calculate the area of a parametric sector

I encountered the following definition: $\forall tD_t=\{(x,y)\in R^2:\theta(x,y) \in [-\pi,t]\}$ where $\theta(x,y)$ is the angle in $[-\pi,\pi)$ that the vector $(x,y)$ forms with the x-axis. ...
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### Understand proofs concerning angles on circles

I am reading the paper "On zeros of convex combination of polynomials" by Fell. In proving a theorem, the author listed two lemmas (Lemma 2 and Lemma 3) without proof. How do we prove the two lemmas?
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### Two circles with a common tangent

Find the angle $\angle BAC$ in the following picture . My attempt : I tried to apply the relationships in the both circles between different angles and arcs in many ways but it didn't work . Also ...
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### How to measure an angle in a polygon that is more than 180?

Assume we have an arbitrary polygon that has no holes nor self edge intersections, but can otherwise be concave and deformed. Assume the vertices are ordered either clockwise or ccw. So for example ...
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### How can I check which face of spherical polyhedron corresponds to a given euler angle?

I am specifically mapping a dodecahedron to a sphere and I am trying to get if a rotator is within the boundaries of a given face. Thank you
84 views

### extracting Angles from a Rotation Matrix

How to extract the angle a from the rotation matrix, given by: ...
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### Requirements of 3 proper Euler angles

Why do proper Euler Angles all come in the form of xyx, yzy, xzx, xyx, and etc? Also, why is the third one needed if it rotates around the same axis as the first one? How I'm seeing it right now, each ...
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### closed form expression for $\sin 10^o$? [closed]

As we know that $\sin 15^o$, $\sin 30^o$,$\sin 45^o$ have simple closed form expressions as these are multiples of 3, but i have never seen any simple closed form expression for $\sin 10^o$ or simply ...
32 views

### Finding a point on a rounded rectangle using an angle

I'm writing an application where I need to be able to plot points onto a rounded rectangle. I know the angle from the center from 0 degrees to where the point needs to be. I need to know the x and y ...
25 views

### Calculate angle

What angle is between vector a and vector b if the angle between vector p and vector q is 90°, where vector p=5a-2b and vector q=-3a-6b? (Yes this is homework)
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### What is the value of $\angle x + \angle y$ in the following diagram?

$\angle p=30^\circ$, $\angle q=45^\circ$, $\angle r=50^\circ$, $\angle$ $s=25^\circ$. $\angle x + \angle y = ?$ Source: Bangladesh Math Olympiad 2016 junior Category I could not find any ways to ...
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### Algorithm for converting a coordinate into angles of a pentagon.

I will go ahead and admit, this might just be something obvious but I did research and couldn't find anything. I have a pentagon, and I know two top points (A & B) and the distance between them (...
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### Is it possible to calculate the sides of a triangle with the angles and the length from tip to base?

Is there an equation to calculate the length of a triangles sides given only the angles and the length from the tip of the triangle to its base? If so please express the equation using the following ...
70 views

### Finding out the value of $\angle DQC$ in a trapezium $ABQD$ where $\angle DCB$ = 30$^\circ$

In this below diagram, $\angle ABC=60^\circ, \angle DCB=30^\circ$, $AD$ is parallel to $BC$ and $AP$ is perpendicular to $BC$. Both the area and perimeter of $ABCD$ and $APQD$ are equal . What is the ...
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### 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 ...
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### 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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### Internal angles in regular 18-gon

This (seemingly simple) problem is driving me nuts. Find angle $\alpha$ shown in the following regular 18-gon. It was easy to find the angle between pink diagonals ($60^\circ$). And I was able to ...
41 views

### When the slope of the angle bisector is 1, is the product of the slopes of the 2 lines forming the angle equal to 1

When the slope of the angle bisector is 1, I have been told that the product of the slopes of the 2 lines forming the original angle is 1. Is this true?
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### Finding the location of points of a triangle given the angle and length ratio.

Given that a point P is located at (-2.5,4.33) I need to locate the points A and B such that $\frac{PA}{PB} = \frac{4.77}{8}$ and $\angle APB = 55^o$. A and B must be on the -ve part of the x axis. ...
46 views

### Signed angle in plane

What is the formula to compute the signed angle between two vectors $u, v\in\mathbb{R}^2$ where positive angle is equivalent to a counter-clockwise rotation on the plane In other words I would like ...
89 views

### Orthogonal unit vector in spherical coordinates

A particle is traveling in the direction of the positive $z$ axis, until eventually, it is deflected. The new direction is given by an azimuthal angle (w.r.t. the positive $z$ axis) $\theta$ and a ...
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### Fast way to compare angles w/o their measures

I need an efficient way to compare the measures of two angles in $\mathbb{R^2}$ that ideally relies on the smallest number of arithmetic operations and no trigonometric operations (no $\arccos$) or ...
36 views

### Finding sign of an angle without calculating the angle itself

Say we have an angle between vectors $P_1$ and $P_2$ in $\mathbb R^2$ whose vertex, $O$, is at the origin. I would like to know the sign of the smallest signed angle between $P_1$ and $P_2$ such that \$...
22 views

### Prepend a vector with 90 degree angle to an existing one

First of all: my knowledge in mathematics is a bit rusty, so no matter how simple my question is, I afraid I in every case need a somewhat detailed answer: I have a line from coordinates (x1,y1) to (...
26 views

### Looking for correlation between length and angle

The problem I'm facing might be rather easy to solve, but I can't think of a way how to do it atm. I want to clip straight 90-degree and some other degree lines. If I clip them at a fixed height (like ...