Law of Tangents
The Law of Tangents is a rather obscure trigonometric identity that is sometimes used in place of its better-known counterparts, the law of sines and law of cosines, to calculate angles or sides in a triangle.
Statement
If and
are angles in a triangle opposite sides
and
respectively, then
Proof
Let and
denote
,
, respectively. By the Law of Sines,
By the angle addition identities,
as desired. $\bluesquare$ (Error compiling LaTeX. Unknown error_msg)
Problems
Introductory
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Intermediate
In , let
be a point in
such that
bisects
. Given that
, and
, find
.
(Mu Alpha Theta 1991)
Olympiad
Show that .
(AoPS Vol. 2)