A sine bar measures angles by turning a length and a height into a right-angled triangle whose geometry fixes the angle.

The bar rests on two rollers set a known centre distance apart; raising one end on a stack of slip gauges tilts the bar, and this centre distance becomes the hypotenuse of the triangle.

The slip gauge stack height is the side opposite the tilt angle, so the angle follows from the sine relation \(\sin\theta = \dfrac{H}{L}\), where H is the slip gauge height and L the centre distance.

With the given figures, \(\sin\theta = \dfrac{50}{200} = 0.25\), so the angle depends on the ratio of slip gauge height to centre distance, exactly as the sine function requires.

Taking the product of height and length (option 2) or their sum (option 4) has no trigonometric meaning and would not yield an angle.

Using the reverse ratio of centre distance to slip gauge height (option 1) inverts the sine relation and would give a wrong angle, so it is incorrect.

Hence, the answer is It is based on the ratio of slip gauge height to the center distance of sine bar.