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).

In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. Angles are also formed by the intersection of two planes in Euclidean and other spaces. These are called dihedral angles. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the spherical angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles.

Angle is also used to designate the measure of an angle or of a rotation. This measure is the ratio of the length of a circular arc to its radius. In the case of a geometric angle, the arc is centered at the vertex and delimited by the sides. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation.

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how to understand angles expressed in rms degree

recently i was going through a system which can detect laser threats arround 360 degree field of view, but the specification says the angle accuracy in rms how to understand this kind of angles,what actually rms means here ? please find the…
kakeh
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What's wrong with the angle trisection using Intercept theorem?

Could anyone tell what I'm missing? I know that angle trisection is proven to be impossible (see Pierre Wantzel in https://en.wikipedia.org/wiki/Angle_trisection). However, I just came up with the following method and can't find any flaw Steps…
xliiv
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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 direction the monster should face when they move). I…
Rick
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Complex numbers: Euler's identity with imaginary angle

Complex numbers can be extended using the polar form $$ Ƶ=re^{i\theta}$$ This allows the complex number to sit on a unit circle, but this is only if theta is a real number. But what if angle theta is imaginery or complex? What does having an…
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The total angle must be $ 90 ^{\circ} $ degrees however as we sum up the each angle , the equation be dishold

I've drawn the above diagram as same as the diagram of the book. The leftmost and the right most arrows make $~90^{\circ}~$ Currently I can't get how the below 2 angles are obtained. $$ \theta_{1}:= \theta_{} + 45 ^{\circ} =\text{angle between…
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Why does direction of vector formula produce same angle, even when exchanging the order of points?

Why does direction of vector formula produce same signed angle, even when exchanging the order of points? For points $P=(x_1,y_1)$, $Q=(x_2,y_2)$ Angle of direction vector is $\arctan(\theta)=\frac{y_2-y_1}{x_2-x_1}$ If we assume for example…
mavavilj
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How calculate the FOV of the faces of a dodecahedron

Having a dodecahedron I want to calculate the field of view (FOV) in degrees of the faces of the shape. If each pentagon has a circunscribed circle, I want to know or how to calculate the angle from the center of the dodecahedron to both sides of…
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What are the implications of the fact that radian measures of angles are real numbers?

Let's say that we proved that the radian measures of angles are real numbers (i.e. if we have an angle $x \text{ rads}$, then $x \in \Bbb R$) since the radian measure of an angle $\theta$ is the length of the arc that subtends an angle of $\theta$…
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Finding angle between two hexagonal planes

I am looking to get angle between two hexagonal planes. I have coordinates of all 12 vertices (2 hexagons). Is there anyway I can find the angle between the planes. And also I have the information about the centers of each hexagonal plane. You can…
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Arranging angle measurements in ascending order

Arrange the following assortment of angle measures in ascending order; 210°, 350°, 2π, 5.3 radians, 90°, 1.7 radians, π/3 , 1 radian, 55°, π. I only just started learning about angle measurements and so I'm struggling with this question. How would…
Savannah
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The expression $2 \sin3x \cos3x = \sin kx$, find the value of $k$

I am supposed to use double angle identity, however, I cant seem to fit any of the equations. I tried saying that the first part of the equation is sin(2x), but I don`t understand why that is incorrect, as $sinx*cosx*2=sin(2x)$. Therefore k would be…
joao leal
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How to find the angles of a trapezoid

The perimeter of a trapezoid is 5 and the lengths of its sides are integers. What are the smallest two angles of the trapezoid. The perimeter is 5 so I get 1*2+1*1+2*1 as the sides. But how do I find out the angles?
Hari
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How to find height of a building from its changing shadow?

The shadow of a building increased by 10 meters when the angle of elevation of the sun decreased by 10 degrees from 70 degrees to 60 degrees. Calculate the height of the building. I tried to construct a diagram, but was unable to make one which had…
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Finding an interior angle between two interior angles

In the picture below; shows how it is illustrated: https://i.stack.imgur.com/XIRfj.jpg I am trying to find angle b; given angles a and c. The value for angle a is 32 degrees, and for c it is 77degrees. How much is angle b? I tried subtracting a and…
Bido262
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Help! In quadrilateral $ABCD$, angle $BAD$ and angle $CDA$ are trisected as shown. What is the degree measure of angle $AFD$?

Help! I have a math problem that's been confusing me a lot. Source: AoPS Staff The problem is: In quadrilateral $ABCD$, angle $BAD$ and angle $CDA$ are trisected as shown. What >is the degree measure of angle $AFD$? This is an image that comes…
Song
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