Law of Tangents - Application

Application

The law of tangents can be used to compute the missing side and angles of a triangle in which two sides and the enclosed angle are given. From \tan = \frac{a-b}{a+b} \tan= \frac{a-b}{a+b} \cot one can compute ; together with this yields and ; the remaining side can then be computed using the Law of sines. In the time before electronic calculators were available, this method was preferable to an application of the Law of cosines, as this latter law necessitated an additional lookups in a logarithm table, in order to compute the square root. In modern times the law of tangents may have better numerical properties than the law of cosines: If is small, and and are almost equal, then an application of the law of cosines leads to a subtraction of almost equal values, which implies a loss of significant digits.

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