HYPOTENUSE of a triangle formed by a steel bar terminating in a cylinder near each end.When one of the CYLINDERS, called a roller, is resting on a flat surface, the bar can be set at any desired angle by simply raising the second cylinder.The required angle is obtained when the difference in height between the two rollers is EQUAL to the sine of the angle multiplied by the distance between the centers of the rollers.\(\sin \theta = \frac{A}{C}\)Apparently, the accuracy of angle MEASUREMENT depends upon the accuracy with which length C, of the sine bar and height h under the roller is known.Now, differentiating h with respect to θ, we have:\(\cos \theta = \frac{1}{C}\frac{{dh}}{{d\theta }} \Rightarrow \frac{{d\theta }}{{dh}} = \frac{1}{{C\;\cos \theta }} = \frac{{\sec \theta }}{C}\)Therefore, the error in angle measurement dθ, due to an error dh in height h is PROPORTIONAL to sec θ.Now sec θ increases very rapidly for an angle greater than 45°. Therefore, it is not recommended to use sine bars for angles greater than 45° because any error in the sine bar or height of slip gauges gets accentuated.