# 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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### 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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### Help calculating angles for woodworking

I am working on a wood working project and need to cut some 2 x 2's on an angle in order to form an X inscribed inside a rectangle. Visually here is what I am trying to create: So basically I want to ...
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### Dynamics of Triangle Iterates by angle bisector

I'm attempting to prove what is demonstrated in this Wolfram demo Let $T_0$ be an arbitrary triangle with vertices $A_0,B_0$and $C_0$,and let $T_1$ be the triangle formed by the intersection points ...
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### 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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### What is the spherical equivalent of splitting a circle into n equal segments and calculating their central angles?

So this is easy to calculate in 2 dimensions, if you have a circle represented by 3 points the angle between any two consecutive points and the spheres centre is simply $\frac{2\pi}{n}$. I basically ...
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### How to find rotated top, left of a rectangle given I have top, left and rotation angle

I think this is a simple problem but my Math/Geometry skills are not very good. I am given the top,left coordinates and the height & width of a rectangle as ...
156 views

### Bounding angles in Riemannian triangles with bounded sides

Is it true that angles in Riemannian triangles with bounded sides are uniformly bounded? More precisely, let $M$ be a Riemannian manifold. Given $0<r <s$, is there a number $\delta$ (...
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### Finding the Point Along a Line Such that an Axis-aligned Box Around the Point Doesn't Exceed Another Line

Given two line segments $L1 = (P1, P2)$ and $L2 = (P2, P3)$, the width and height $(W, H)$ of a rectangle, and the angle between $L1$ and $L2$ $(\phi)$, how would I determine the point $Q$ on L1 such ...
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### Calculate Third Point of Triangle knowing Vector

I have 3 points and their coordinates $(A, B, C)$. Then I have new coordinates of points $A'$ and $B'$ How to calculate the coordinates of point $C'$ knowing that the distance from point A to point C ...
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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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### 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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### 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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### How to calculate solid angle of nonspherical surface?

My objective is to calculate (or find an expression) for the solid angle of a circular loop (parametrized by $(x,y)=(r \cos{x_i}, r \cos{y_i})$, where $0\leq x, y \leq 2\pi$) on the surface defined as:...
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### Height of a Triangle, and a Progression of Triangles

I am researching some algorithms and it turns out that the following figure I made can model what is happening in a "step". I am not a mathematician, so I was having a hard time with this one. The ...
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### How to find change in angle when vertical Scale of depth axis is modified?

Let Q be the Quaternion that perform a rotation of angle degrees around some axis of rotation. Later I change vertical exaggeration of my Vertical axis (z) to some value VS, e.g. make the vertical (z) ...