# 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).

831 questions
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### How to convert Euler's angles and a radius to spherical coordinates?

I'm working on simple blender (3d modeling software) add-on, and I need to convert Euler's XYZ rotation and a radius value to spherical coordinates (The center of a sphere is at (0,0,0)). How to?
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### How can I define a percentage from another percentage between a specific interval

I have a cube that rotates. When the rotation is at 45 degrees I need to scale the cube to 90% of its size. My struggle here is to calculate the amount of percentage to scale the cube according to ...
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### How would I rotate an Euler angle?

Given an orientation given as an Euler angle, how would I rotate this Euler angle? I assume simply multiplying the angle with a rotation matrix is not a valid approach. For example I am measuring an ...
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### Complete characterization of equiangular polygons with two alternating edge lengths

I am looking for a complete characterization of equiangular polygons with two alternating edge lengths. Also self-intersections are allowed (as seen here https://en.wikipedia.org/wiki/Isogonal_figure ;...
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### Find the value of the angle $X$ in the given figure [closed]

In this picture, the curve in the inside of the big outer triangle is actually its incircle. The edges of the triangle inside the incircle are the intersections of the incircle with the outer triangle....
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### Rotate one 3D vector on another

I have a mathematical problem which is part of my 3D game and I can't seem to be able to figure it out. I have two three-dimensional vectors a and ...
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### Why must the coordinates of a point on a circle be sinusoidal as a function of the angle? [closed]

A defining feature of radians as a unit of measurement is that if an angle $\theta$ is expressed in radians, the height of a point on the unit circle at this angle is $\sin(\theta)$. Is it possible ...
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### Right Circular Cylinder: Distance between axis and plan

B is a point in the top circle of a right circular cylinder. C is a point in the bottom circle of the given cylinder. The angle between [BC] and the base's plan of the cylinder is 45 degrees. The ...
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### Absolute Value of Vector with only 2 values and one Angle?

How do I calculate the absolute Value of a Vector when I only know the Values of two Vectors and the angle between them? The Vector I wanna find is the resulting Vector after you add the other 2. ...
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### Is it given that two lines are parallel if a right angle is shown?

If I have a diagram, like the following: And I want to make make a proof for something like how segment AB is $\cong$ to segment AC if segment BD $\cong$ segment DC (using Perpendicular Bisector ...
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### finding third point, provided two points , an angle and the length from one of two given points

I have gone through many of the answers and I have not a suitable one so I am asking this question As provide in the reference image I have been provide two points A(x, y) and B(x,Y), an angle Θ ...
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### Trigonometry Angle Addition and Subtraction

I'm working on a problem. The problem is boxed in Blue. Ignore the right side boxed in green, it's unreleated. Inside the blue box, I have highlighted in green where my error is when solving this ...
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### Scale cosine similarity between vectors to range 0, 1?

I am interested in calculating similarity between vectors, however this similarity has to be a number between 0 and 1. There are many questions concerning tf-idf and cosine similarity, all indicating ...
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### If a right circular cone has three mutually perpendicular generators then find its semi-vertical angle.

If a right circular cone has three mutually perpendicular generators then find its semi-vertical angle. We see that if $ax^2+by^2+cz^2+2fyx+2gzx+2hxy=0$ has three mutually perpendicular generators, ...
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### 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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### rotate plane according to pitch,yaw and roll

Lets say, i have ground-plane equation = $ax + by + cz + d$ . Then, i rotate camera and i know new yaw ( $\theta$ ), pitch ( $\alpha$) and roll( $\gamma$) angle of camera. How can i calculate new ...
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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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### 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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### 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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### 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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### 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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### 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 ...