# 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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### What is the angle between the median and the bisector?

In a triangle ABC, what is the angle $\theta$ between the median AM and the bisector AD? I want a way to know the measure of that angle, given the lenghts of the sides and angles of the triangle. I ...
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### Proof of $\angle$ sum of polygon.

First, I know this question might have been asked by several times, see here, for an example. Before someone may want to mark it as dulplicate, I would like to calrify what I want to ask. Mainly, I ...
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### Why doesn't the average angle made by a function with the $x-axis$ work as expected?

The average angle made by a curve $f(x)$ between $x=a$ and $x=b$ is: $$\alpha=\frac{\int_a^b\tan^{-1}{(f'(x))}dx}{b-a}$$ I don't think there should be any questions on that. Since $f'(x)$ is the value ...
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### Similar Triangles Problem (No corresponding sides)

This problem is from a Year 9 Oxford Maths textbook. I have tried to solve it since yesterday to no avail. Here are the questions - It is only (b/c) that I cannot solve, but I included the other ...
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### Counter-clockwise angle between edges

I have a couple of connected lines (or rather edges) in the form of coordinates, that is for each edge a starting point $(x_s,y_s)$ and end point $(x_e,y_e)$. and I want to know a specific angle ...
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### Angle of circular droplet

I am trying to find the angle $\theta$ of the following droplet: I think using $\tan$ is the right way to go, and I thought of using it on the angle formed by the line $r$ and $b$. However, that ...
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### How to calculate the quaternion from/and axis angle having parent and target position (camera and its target)?

I want to calculate the orientation (quaternion) of the virtual 3d camera that is looking at some point in 3d space. The illustration: According to this explanation the quaternion be calculated from ...
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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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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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?...
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### 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 ...
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### Angles between vectors of center of two incircles

I have two two incircle between rectangle and two quadrilateral circlein. It's possible to determine exact value of $\phi,$ angles between vectors of center of two circles.
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### Pythagoras: Get b when only a and angle α are given

Given the Pythagoras Theorem: a² + b² = c² Is there a way to get the value of b when we only have a value for a and the angle α? To be frank, I have no clue about that, what I want isn't the angle ...
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### Why do we use degrees? [closed]

I see a lot of people who ask why we use radians instead of degrees. But why do we use degrees instead of radians. In the cases we use degrees instead of radians, what convenience does it bring? The ...
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### Find the $\angle ACB$ of $\triangle ABC$.

If $PC=2BP$, $\angle ABC= 45^\circ$, and $\angle APC=60^\circ$, find $\angle ACB$. All solutions are acceptable but please try solving using reflection of point $C$ through the line segment $AP$. I ...
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### How to convert components into an angle directly (for vectors)?

Let us say we have a vector with $x$-component $-2$, and $y$-component $-1$. We have the equation: $$\tan\theta=\frac{-1}{-2}$$ So if we take the inverse of $\tan$ of $\frac12$ we get $26.565^\circ$....
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### We have angle=arctan(dy/dx), but what happens when dx=0?

Here is a formula: $\text{angle}=\arctan(dy/dx)$. I can find an angle with my calculator for any value except $dx=0$. My question is: is there no angle or, is there something that says when $dx=0$ ...
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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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### How to evaluate $\cos{\frac{\pi}{8}}$?

I have to evaluate $\cos{\frac{\pi}{8}}$ and I'm supposed to do so evaluating first $\cos^2{\frac{\pi}{8}}$ (since it's an exercise to practice half-angle formulas). Solving this second formula I get ...
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### Prove that for every $n\ge3$ there exists a convex $n$-gon with exactly 3 acute angles

I'm really not sure where to start. Induction can really be used, and that seems like the only way to prove for all $n$.
The question which I was trying to solve is: Find the time between four and five o' clock when the angle between the hour hand and the minute hand is $78^\circ$. My approach: At four o' clock, the ...