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 
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.
Read more about this topic: Law Of Tangents
Famous quotes containing the word application:
““Five o’clock tea” is a phrase our “rude forefathers,” even of the last generation, would scarcely have understood, so completely is it a thing of to-day; and yet, so rapid is the March of the Mind, it has already risen into a national institution, and rivals, in its universal application to all ranks and ages, and as a specific for “all the ills that flesh is heir to,” the glorious Magna Charta.”
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)
“May my application so close
To so endless a repetition
Not make me tired and morose
And resentful of man’s condition.”
—Robert Frost (1874–1963)
“The best political economy is the care and culture of men; for, in these crises, all are ruined except such as are proper individuals, capable of thought, and of new choice and the application of their talent to new labor.”
—Ralph Waldo Emerson (1803–1882)