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If I understand the question correctly, it is about the component of a vector along the axes, with the angle measured from the positive direction of the x-axis. If so, sin is used on the y-component.
It is the distance, measured in the vertical direction, using centimetres as the unit of measurement. The vertical direction in a book is normally taken to be the direction from the bottom of the page to the top. Otherwise it is taken to be along the radius of the earth at that location.
The slant height of an object is the distance measured along a lateras face from the base to the apex . It is measured in the center of the face.
Yes, it is a Continuous variable measured along an equidistant scale.
Yes.