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 Can I Calculate Irregular Polygon's Internal Angle? [closed]

For example there is irregular polygon and I choose a vertex and I want to calculate it's interior angle, the angle can be more than, less than or equal 180 degrees. How can I calculate and how can I ...
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1 vote
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Sum of "angles" of a 3D tetrahedron

We know that the sum of angles of a triangle equals the straight angle (180 degrees). Can we convert a 2D theorem to 3D? e. g. We can generalize the triangle to a tetrahedron, angles of the triangle ...
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solve for the unknown in each triangle given and round it to the nearest tenth using the law of simes [closed]

this is the triangle one and two. find the missing or unknown in each triangle so that the triangle will be completed
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2 votes
1 answer
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Finding angle in circle to produce equal areas

I have a circle that is divided into 4 quadrants with a vertical and a horizontal axis. The center of the circle (where the axes cross) is point b. The top of the vertical axis is point d. On the ...
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3 votes
1 answer
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Calculating the angle between 2 one-sided surfaces.

For a piece of software that I am writing, I need to determine the angle between two 3-dimensional one-sided surfaces that intersect at a line. The surfaces are defined as triangles with a normal ...
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MSE of the Phase Estimation of a Noisy Complex Quantity

Presentation of the Problem I am making a measurement which yields me the complex quantity: \begin{equation} S_k = e^{i \cdot \phi} + X_k + i \cdot Y_k \quad \text{with} \quad X_k, Y_k \stackrel{iid}{...
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Calculate Intersection point of 2 Lines with angle [closed]

I would like to calculate an intersection point of two lines in a 2D area. I think it should be really simple but i cannot figure it out. I have two points P1(x,y), P2(x,y) and 2 angles alpha and beta....
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Solving angle relationships in triangles with limited information

What is the relationship between angles $\angle abd$ and $\angle acd$, when line $bc=\frac{1}{2}$ and line $ac=30$? b c and d are in a straight line, and point d is a right angle The answer should ...
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Locus of a trajectory [closed]

If a stone is thrown at an angle of elevation of 45 degrees. What would be the locus of its trajectory? How would you sketch this? Problem The answer appears to be the arc of a circle, but shouldn't ...
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Angles of a Quadrilateral

I have a quadrilateral ABCD. If I know the angles $DAB, DCB, ADB, CDB, ABD, CBD$, can I obtain the angle $DAC$? I know that I can do it by some coordinate geometry or the sine formula, but is there a ...
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Formula of an area of sector of circle without notating a radius of a circle

The following quotes are from this book(A First Course in Calculus by Serge Lang) Suppose we are given a continuous function $$r=f(\theta)\tag{1}$$ which is defined in some interval$~a\le\theta\le b~$...
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APMO 2020 Geometry Problem | Proving lines to be concurrent

PROBLEM Let $\Gamma$ be the circumcircle of $∆ABC$. Let $D$ be a point on the side $BC$. The tangent to $\Gamma$ at $A$ intersects the parallel line to $BA$ through $D$ at point $E$. The segment $CE$ ...
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Which coordinates go first when calculating an angle from point A to point B?

I'm trying to design a 2D game and am working on monster movement right now. I need to calculate the angle a monster moves towards when they move from location A to location B (so I know which ...
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Angles of Triangle in Two Coordinate Systems

If I know the coordinates of three points in a known coordinate system, I can calculate the angles of a triangle that includes those three points. However, if I observe the same three points in an ...
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Projecting 2D coordinate into 3D space with camera matrix

I am not entirely sure that this is the right place to ask or if my problem is solvable, but I am out of ideas and googling hasn't brought me any closer to a solution unfortunately. Again if anyone ...
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1 vote
1 answer
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To which angle do the wheels have to turn relative to their current position in order to turn correctly toward the object?

I am trying to write an algorithm to turn the EV3 robot (https://d2nmr6p48f8xwg.cloudfront.net/content_pictures/pictures/000/001/570/814c51fb41fab7a3e3039ec6a067accc510a9341Lego-Mindstorms-Ev3-Car-...
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Negative angle in radians [closed]

I compute an angle of a vector in radians and it is negative (<0, for example _ -5, -150..) I am going to use cordic to compute sin and cos. For cordic I use the full circle ( 0 - 360), positive ...
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Are there indicators for rads, just like the indicator ° is for degrees?

I am using a formula which calculates an angle $ θ_{h} $, and I am not sure if the result is (as I suspect) rad $\times$ degrees: $$ θ_{h}=\dfrac{π}{2}\sin^{-1}\left(\dfrac{2}{π}-0.2782\right) = \...
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1 vote
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In any 3d object, how do you calculate the rotation of that object so the visible part with most surface area is pointing to the camera/eye?

Example: Take a sphere and cut it in half. If you point the curved part of the half sphere to the camera its the visible part with most surface area
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How to compute inner angles of polygons

I'm currently implementing an algorithm to split a concave polygon into y-monotone polygons, so I can triangulate those. As I writing this for my own little library, I'm implementing one of the ...
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1 vote
2 answers
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Find theta given point on circle

I am having trouble visualizing and understanding how you might obtain an angle given a point on a circle. I have a $(x, y)$ point where the values range between $0,1$ for both $x,y$. How would I ...
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How to solve $\beta = \alpha - \arcsin(k \cdot \sin(\alpha))$ for $\alpha$?

I'm looking for an analytical expression in the form of $\alpha = f (\beta)$, so solving the equation below for $\alpha$. Is this possible? $$\beta = \alpha - \arcsin(k \cdot \sin(\alpha))$$
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2 votes
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Angle between vectors in $\mathbb{C}$

I know that in $\mathbb{C}$ $$\cos\measuredangle(x,y)=\frac{|Re(\langle x,y\rangle)|}{\|x\|_2\|y\|_2}.$$ Now I want to show that $$|\sin\measuredangle(x,y)|=\frac{\|y-\lambda x\|_2}{\|y\|_2},$$ $\...
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2 answers
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Find angle QTS.

Given $PQ=PR, QT = 2SU$, $PS \parallel QR$ and $SU \perp QR$. $QT$ is angle bisector of $\angle PQR$. What is the size of $\angle QTS$? What I have so far: $\angle PQT=\angle RQT=\alpha$, $\angle QRP =...
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Find the distance between two towers/building

Mr Gray stood on top of the CN tower and spotted a Casa lama, his angle of depression is 6 degrees. He then turned around 110 degree and found CNE. His angle of depression to CNE is about 9 degree. ...
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3 votes
4 answers
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Solve a triangle given one angle of the median, and a side and an angle of its external triangle

This is a modified version of this question, and as such I'm using similar wording and visuals. Given: $α_2$, one of the two angles which the vertex $A$ is split by the median $m$; $\overline{AD}$, ...
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How to calculate this inside triangle angle?

Is it possible to calculate the angle X, without knowing the upper angle value for blue triangle?
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How to detect witch direction would be the closest between 2 angles

I want to get the fastest direction (+ or -) to move into a new angle. I tried this : (newAngle - oldAngle) % PI If the value is positive, then I have to use ...
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0 votes
3 answers
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Calculate difference of two numbers on the 360 circle with the sign/direction

There are a couple of answers to this question, but they leave out the sign. Is there a clever way to determine if the angle is positive or negative? This nice formula gives the angle, but not the ...
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Expressing an inclination angle in another coordinate system

A vector is pointing at angles $\theta_1$ and $\varphi_1$ defined in a coordinate system XYZ, $\theta_1$ being the inclination angle (relative to Z axis) and $\varphi_1$ the azimuthal angle (in the XY ...
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1 answer
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How the rotatable airplane-attached-camera exactly photographing the ground?

An airplane is flying horizontally on a straight line at a speed of$~1000~\mathrm{km}/\mathrm{hr}~$, at an elevation of$~10\mathrm{km}~$. An automatic camera is photographing a point directly ahead on ...
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Clarifying a right angle in a bisected triangle

Here is a question that I was doing this morning: Part of the mark scheme makes use of the following: My question: How do we know that the bisector of the angle DAB meets the midpoint at a right ...
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From the top of a cliff 160m high, two buoys are observed. Calculate the distance between the buoys.

From the top of a cliff 160m high, two buoys are observed. Their bearings are 337° and 308°. Their respective angle of depression are 3° and 5°. Calculate the distance between the buoys. I got this ...
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How do I find the relative angle between two ordered sets of points?

Say I have two sets of ordered points, $(x_1, y_1)$ and $(x_2, y_2)$, and $(x_3, y_3)$ and $(x_4, y_4)$. I want to map the first pair of coordinates to the second pair of coordinates (so the first ...
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1 vote
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Guessing rectangle hypotenuse angle from proportion between it's sides

if a rectangle has it's width as double it's height, can I assume that his hypotenuse will divide the his angle in a proportion of 2:1, or as the angle is 90, the angles would be divided so one part ...
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1 answer
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Show that the curves $r^2 = a^2\cos^2(\theta)$ and $r = a(1+\cos(\theta))$ intersect at an angle $3\arcsin((3/4)^{1/4})$. [closed]

Show that the curves $r^2 = a^2\cos^2(\theta)$ and $r = a(1+\cos(\theta))$ intersect at an angle $3\arcsin((3/4)^{1/4})$. I know how to solve this question but I am not getting the angle to be the ...
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0 votes
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Mutual angles between a set of vectors

I have $7$ unit vectors in $3$D space. Suppose we know the angles between some pairs of vectors. The graph below shows the known angles as edges. For example we know the angle between vectors '$3$' ...
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Ange bisector - how to choose bisector of interior angle

Let points A,B,C be the vertices of the triangle and vertex B be also a vertex of angle we want to divide. Inspired by construction I derived following way to write equation for angle bisector :- ...
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Find the angle -- Geometry Quetion

The question is from primary school Mathematics competitions. It looks easy, but so hard to find the angle using elementary school knowledge. In the diagram below, ABC is a triangle with $\angle BAC=...
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1 vote
2 answers
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"A Function Reduces by the Greatest Quantity in the Direction of it's Derivative" - How do we know this?

We are always told that "A Function Reduces by the Greatest Quantity in the Direction of it's Derivative" - but how exactly do we know this? I tried looking into this and came across ...
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1 vote
1 answer
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Creating a change in X and Y with an angle.

I am coding a small game in JavaScript and I am running into a math problem. I am trying to move an object towards the location that I just clicked. I am able to successfully do this with the code ...
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1 vote
1 answer
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What does it mean by a force acting horizontally?

Question: A body of $10kg-wt$ is kept in an equilibrium condition by a force of $5kg-wt$ acting horizontally, a force of $F\ kg-wt$ acting at an angle $60^{\circ}$ with the horizon and a force of $R\ ...
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1 vote
1 answer
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What does $\cos(\pi-\overline{B+C})$ mean?

Here $A$, $B$ and $C$ are three angles of a triangle, so $A+B+C=\pi$. Now, my book did the following: $$\cos A$$ $$=\cos(\pi-\overline{B+C})\tag{1}$$ $$=-\cos(B+C)$$ My comments: In $\cos(\pi-\...
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1 vote
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Can the angle between two vectors be negative? [duplicate]

Question: The angle between two vectors $\vec{P}$ and $\vec{Q}$ is $\alpha$. If $\tan\alpha=-\sqrt{3}$, determine $\alpha$. My attempt: $$\tan\alpha=-\sqrt{3}$$ $$\alpha=\tan^{-1}(-\sqrt{3})$$ $$\...
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0 votes
1 answer
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Why is this angle taken as negative?

Question: The resultant of two concurrent forces, $\vec{P}$ and $\vec{Q}$, $[P>Q]$, trisects the angle between them. Show that the angle between them is $3\cos^{-1}\left(\frac{P}{2Q}\right)$ and ...
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1 vote
0 answers
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How is my book finding the magnitude of the resultant differently?

Question: Forces of magnitude $Q-R$, $Q$, $Q+R$ act at a point in directions parallel to the sides of an equilateral triangle taken in order. Find the magnitude of their resultant. My attempt: Let $$...
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1 vote
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Angle between plane and line

I'm getting a really large angle when I work out this problem and I'm not sure why. I have a plane which has the equation: $0.19x-0.68y+0.7x = -2.19$. I took a point which is on the plane and called ...
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Distance between two objects given their angle of depression

A boat is situated between a lighthouse and a ship such that all three of them are in a straight line. If the angles of depression of the boat and the ship from the top of the lighthouse $20$ meters ...
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3 votes
4 answers
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How does the angle of an isosceles triangle change as you increase the height

$ABC$ and $ADB$ are isosceles triangles. Given $\beta,$ $R$ and $h$, how can I find angle $\alpha$? $\beta$ is the top angle of the triangle $ABC$, so $\angle{ACB}$. $h$ is the change in height ...
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1 vote
3 answers
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Find the length of OB in triangle ABC [closed]

In a $\Delta ABC$, $O$ is a point in its interior such that $OA=12$cm, $OC=9$cm and $\angle AOB=\angle AOC=\angle BOC$ and $\angle ABC=60^\circ$. Then what is the length of $OB$ (in cm)? 6√3 4√3 4√6 ...
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