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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Where exactly do radians come from?

I'm aware that the angle in radians is 1 when the arc length is equal to the radius. However, I wonder if this is exactly where radians come from. Have we set radians like this (like we set $i^2$ to $-1$) or is there something more to it?
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What is the smallest angle of given triangle?

Calculate the smallest angle in a triangle with side lengths 7 cm, 8 cm and 9 cm. A. 35∘ 20′ B. 58∘41′ C. 60∘ D. 48∘19′ do i need Trigonometric ratios table?
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Corelated angles help

So I am asked to use the appropriate compound angle formula to create an equivalent expression for tan(-15). my solution was: \begin{align}\tan(-15) &= \tan(30-45) \\ &=\frac{\tan30 - \tan45}{ 1+\tan30 \cdot \tan45} \\ &=…
ernest
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Is there such a thing as a $0^\circ$ angle?

I am curious if there is such a thing as a zero degree angle, and if so, what does it look like? I am also wondering if a zero degree angle equals a $360^\circ$ degree angle? I understand that a $360^\circ$ angle is essentially a circle, or the…
CandidFlakes
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