ABSTRACT

In any triangle (in a plane) with sides a, b, and c and corresponding opposite angles A, B, C, a sin A = b sin B = c sin C   Law     of   sines https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq76.tif"/> a 2 = b 2 + c 2 − 2 c b   cos   A   Law     of     cosines https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq77.tif"/> a + b a − b = tan 1 2 ( A + B ) tan 1 2 ( A − B )   Law     of   Tangents https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq78.tif"/> sin 1 2 A = ( s − b ) ( s − c ) b c ,       where     s = 1 2 ( a + b + c ) . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq79.tif"/> cos 1 2 A = s ( s − a ) b c . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq80.tif"/> tan 1 2 A = ( s − b ) ( s − c ) s ( s − a ) . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq81.tif"/> A r e a = 1 2 b c   sin     A                         = s ( s − a ) ( s − b ) ( s − c ) . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq82.tif"/>