two triangles are similar
... has volume 320cm3, what is the volume of large pyramid? A “square can” is a right cylinder that has height equal to its diameter. One square can has height 5cm, and another has height 12 cm. About how many full cans of water from the smaller can are needed to fill the larger one. ...
... has volume 320cm3, what is the volume of large pyramid? A “square can” is a right cylinder that has height equal to its diameter. One square can has height 5cm, and another has height 12 cm. About how many full cans of water from the smaller can are needed to fill the larger one. ...
Name 1303 - Qz # 1, January 18, 2001
... Given a circle we say an angle is a central angle if its vertex is at the center of the circle. measure of an angle: look at two ways of measuring an angle radian measure: to be discussed later for now Given a circle of any radius r, construct a central angle so the intercepted arc of the circle i ...
... Given a circle we say an angle is a central angle if its vertex is at the center of the circle. measure of an angle: look at two ways of measuring an angle radian measure: to be discussed later for now Given a circle of any radius r, construct a central angle so the intercepted arc of the circle i ...
Euler angles
The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body. To describe such an orientation in 3-dimensional Euclidean space three parameters are required. They can be given in several ways, Euler angles being one of them; see charts on SO(3) for others. Euler angles are also used to describe the orientation of a frame of reference (typically, a coordinate system or basis) relative to another. They are typically denoted as α, β, γ, or φ, θ, ψ.Euler angles represent a sequence of three elemental rotations, i.e. rotations about the axes of a coordinate system. For instance, a first rotation about z by an angle α, a second rotation about x by an angle β, and a last rotation again about z, by an angle γ. These rotations start from a known standard orientation. In physics, this standard initial orientation is typically represented by a motionless (fixed, global, or world) coordinate system; in linear algebra, by a standard basis.Any orientation can be achieved by composing three elemental rotations. The elemental rotations can either occur about the axes of the fixed coordinate system (extrinsic rotations) or about the axes of a rotating coordinate system, which is initially aligned with the fixed one, and modifies its orientation after each elemental rotation (intrinsic rotations). The rotating coordinate system may be imagined to be rigidly attached to a rigid body. In this case, it is sometimes called a local coordinate system. Without considering the possibility of using two different conventions for the definition of the rotation axes (intrinsic or extrinsic), there exist twelve possible sequences of rotation axes, divided in two groups: Proper Euler angles (z-x-z, x-y-x, y-z-y, z-y-z, x-z-x, y-x-y) Tait–Bryan angles (x-y-z, y-z-x, z-x-y, x-z-y, z-y-x, y-x-z). Tait–Bryan angles are also called Cardan angles; nautical angles; heading, elevation, and bank; or yaw, pitch, and roll. Sometimes, both kinds of sequences are called ""Euler angles"". In that case, the sequences of the first group are called proper or classic Euler angles.