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We know that sin @ = h/l is the basic principle of working of sine bar.

Differentiating above equation,

.

. . cos @ . d@ = l.dh - h.dl

_________ l*l

d@ =tan@(dh/l - dl/l)

This indicate that error is a function of tan @ and below 45 degree error is smaller which suddenly increases above 45 degree. because of this reason sine bar is preferred for measuring angle below 45

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