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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How to express an angle between two angle bisectors in interior angles of a convex quadrilateral?
Given a convex quadrilateral $ABCD$, I would like to express the angle between angle bisector of internal and external angles of the opposite vertices in interior angles of $ABCD$.
Here is the drawing ...
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2D angle from known 3D angle. [closed]
I have $2$ vectors in $3$D space: $\hat{u}$ and $\hat{v}$.
The angle between them is $\varphi$, so that
$$
\hat{u}\cdot\hat{v} = u_{x}v_{x} + u_{y}v_{y} + u_{z}v_{z} =
\cos\left(\varphi\right)
$$
...
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Advance Angle Chasing [closed]
In acute triangle ABC, with AB<AC, H is orthocenter, O is circumcenter. Let m(OBC)=$a$, and m(OCA)=$b$
What is the value of m(AHO) in $a$ and $b$
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How to prove opposite angle bisector theorem for convex quadrilaterals?
Let $ABCD$ be a convex quadrilateral with $BL$ and $DL$ be its angle bisectors. I want to know how to prove that the acute angle $\alpha$ between these bisectors is equal to $\frac{\left|\angle A - \...
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solution-verification | show that $[BN$ is the bisector of the angle $\angle VBC$
The problem
Let $VABCD$ be a regular quadrilateral pyramid with peak $V$. The plane $\alpha$ contains the line $AB$ and cuts $CV$ and $DV$ at the point $M$, respectively $N$. If $P$ is the midpoint of ...
- 748
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Find the value of the interior angles of a polygon [closed]
I have coordinates of points $(x, y)$. By connecting these points we get a polygon in which I have to get values of its internal angles.
For example points = $[3,1], [3,3], [1,3], [3,5], [7,5], [7,1]$
...
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lower bound of $\sum \cos^k(\theta_i-\theta_j)$
In this question, Lower bound of sum of cosine of angle difference, the lower bound $\sum_{i,j\in [n]}\cos^2(\theta_i-\theta_j)\geq \frac{n^2}{2}$ is given in the answer.
I am wondering, what is the ...
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Find the Cosine of the Angle Between the Plane $(MND)$ and the Plane $(ABC)$
The problem
Consider the cube $ABCDA'B'C'D'$. Let $M$ be the middle of $AA'$ and $N$ the middle of $B'C'$.
a) Determine the tangent of the angle between $AD'$ and $MN$
b) Find the cosine of the angle ...
- 748
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solution-verification | Calculate the sine of the angle between two side faces of a trunk
The problem
Let the trunk be a regular quadrilateral pyramid $ABCDA'B'C'D'$ with the side of the large base of $8$ cm and the side of the small base of $4$ cm. The lateral faces are isosceles ...
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Determine the measure of the angle of the planes $(NBC)$ and $(ABC)$
the problem
Let the triangle $ABC$ with $\angle A=30, \angle B=15, AC=2a$ and $M$ be the midpoint of $AB$. At point M we construct the perpendicular to the plane of the triangle on which we take point ...
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lower bounding $\Big\{\Big(\sum_{i\in[n]}\sum_{j\in[n]}\cos(\theta_i-\theta_j)\Big)^2-{\sum_{i\in[n]}(\sum_{j\in[n]}\cos(\theta_i-\theta_j))^2}\Big\}$
Consider
$$S(\theta):=\Big\{\Big(\sum_{i\in[n]}\sum_{j\in[n]}\cos(\theta_i-\theta_j)\Big)^2-{\sum_{i\in[n]}(\sum_{j\in[n]}\cos(\theta_i-\theta_j))^2}\Big\}$$
Motivation.
I am curious about the minimum ...
- 1,052
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Parallel line equation
I want to incorporate 2 diagonal lines in a logo design. The lines have to be parallel to each other and have to be exactly 0.5 inches apart when measured perpendicular. The upper point of Line 1 has ...
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computing elevation angle of a object on a circular fisheye image
I'd like to calculate the elevation angle of an object at any given coordinates (x,y) of the image that has been taken with a circular fisheye lens (185° of fov). By elevation angle, I mean the angle ...
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How to calculate the clockwise rotation (bearing) from 3 known coordinates and independent of the cartesian XY axes
Greetings Maths experts,
I come to you once more looking for mathematical assistance to help me solve another challenge in my CAD software.
Background Info:
I'm trying to write a VBA macro which will ...
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How do I prove that the angle between two 2d vectors depends of sign of dot product of two 2D.?
How would you prove that given two 2D vectors in the $\vec{v} = \begin{bmatrix}
v_{1} \\
v_{2} \\
\end{bmatrix}$ and $\vec{u} = \begin{bmatrix}
u_{1} \\
...
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