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§4.42 Solution of Triangles

Contents

§4.42(i) Planar Right Triangles

See accompanying text
Figure 4.42.1: Planar right triangle. Magnify
4.42.1 sinA=ac=1cscA,
4.42.2 cosA=bc=1secA,
4.42.3 tanA=ab=1cotA.

§4.42(ii) Planar Triangles

See accompanying text
Figure 4.42.2: Planar triangle. Magnify
4.42.4 asinA=bsinB=csinC,
4.42.5 c2=a2+b2-2abcosC,
4.42.6 a=bcosC+ccosB
4.42.7 area=12bcsinA=(s(s-a)(s-b)(s-c))1/2,

where s=12(a+b+c) (the semiperimeter).

§4.42(iii) Spherical Triangles

See accompanying text
Figure 4.42.3: Spherical triangle. Magnify
4.42.8 cosa=cosbcosc+sinbsinccosA,
4.42.9 sinAsina=sinBsinb=sinCsinc,
4.42.10 sinacosB=cosbsinc-sinbcosccosA,
4.42.11 cosacosC=sinacotb-sinCcotB,
4.42.12 cosA=-cosBcosC+sinBsinCcosa.

For these and other formulas see Smart (1962, Chapter 1).