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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What is the advantage of measuring an angle in radian(s)?

What is the advantage and use of measuring an angle is radian(s) compared to degree(s)? My book suddenly switched to radian(s) for measuring an angle in this grade and I do not know why.
MrAP
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Find the bearing angle between two points in a 2D space

I continue developing a 2D Collision Detection System in a programming language (Javascript) and one of the last things I need to sharpen it is to know a formula to find this angle: NOTE: X and Y increase their value FROM LEFT TO RIGHT AND TOP TO…
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What is the angle of a point?

I had a question in my test: "The sum of angles at a point is________. (A) 0; (B) 360; (C) 90; (D) 180;" I feel that since there are no angles or rays drawn at the point in the first place, the answer can't be 360, but that is the correct answer for…
aravk33
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Ambiguous Times in a 12 hour period

I just had this question in a maths competition. I came to 132 as an answer but I wasn't able to formally show that the answer is correct. Can anyone solve this following problem formally? Suppose there is a clock that has its minute and hour hands…
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Cardinality of set containing points on a circle such that = i * 1 radian?

I'm on a conversion MSc and haven't done math in a while, so apologies if this is an easy Q but I'm stumped. I've literally only just learned what radians and sets are- I think I've done a decent job of getting the basics of each, but I'm struggling…
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How valid a method of measuring angles is this?

The three basic angle measurement systems i.e. sexagesimal, centesimal and circular systems are based on a common idea of measuring angles in terms of arc lengths and radii. Some terminology : An angle is formed by rotating a "side" about a point.…
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How many angles can be drawn using only a ruler and a compass?

So far I know that it’s possible to draw angles which are multiples of 15° (ex. 15°, 30°, 45° etc.). Could anybody please tell me if it's possible to draw other angles which are not multiples of 15° using only a compass and a ruler.
Russell
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Finding the angle between two points given their Azimuth and Elevation angles

I have two points in the sky and I have their coordinates in Azimuth and Elevation angles with respect to position O. I want to find the scalar angle between the two points w.r.t. position O. Thank you so much for your help!
Viki
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How to find angle of arc given arc length and sagitta?

Given the length of an arc and the length of sagitta, can you calculate the angle (radians)? I struggle to work out all the parameters I need. For instance, to calculate the radius I need the length of the sagitta and the chord length (but I don't…
thomthom
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What is the word for the relationship between two angles that add up to 360˚

If A+B = 180˚ they are supplementary to each other but what would you call their relationship if they add up to 360˚?
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Do Zero degree angles exist?

If an angle is the measure of distance between to points (Edit: Ok, admittedly bad phrasing. A measure of rotation between two intersecting lines, or points, etc.), is there such a thing as a zero degree angle? I asked a math nerd friend about this…
Ken X
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An angle between $[0, 360°[$ or $[0, 2\pi[$ is called a normalized angle. But how is called one expressed between $[-180, 180°[$ or $[-\pi, \pi[$?

For a computational calculation, I need to express my resulting angles between $[-\pi, \pi[$. I am in search of an API easing me reaching this expression, when it happens that my results are outside this interval. But I don't know what term querying…
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Calculate distance from one angle to another in different directions

I've an object whose rotation degrees are locked to be in the interval $[0, 360)$. I want to calculate the distance in two different directions, so that I can decide which is the shorter route for a spinning. That is, in a -1 scale (anticlockwise),…
Hydroper
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How to measure the angle of this Pyramid/Prism/Tent like shape?

I was designing this model with glasses. The front triangle sides are $a, b$ and $c$. And the slant height is $h$. The top length is $l$ and bottom full length is $L$. One value that is fixed is the back side triangle angle i.e.…
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Finding azimuth and zenith angles for tetrahedron

I have an irregular tetrahedron as shown in figure below, and I know the length of all of its edges. I want to find the azimuth and zenith angles $\phi$, and $\theta$ for vector $C$. I managed to find the zenith angle $\theta$ by finding the volume…
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