Laturile se vor afla DOAR prin Teorema lui Pitagora. La punctul a) voi scrie mai complex Teorema si functiile trigonometrice, iar la celelalte voi scrie mai direct.
a) ΔABC-dr[tex]T.P.\\==>[/tex]
[tex]BC^{2} =AB^{2}+AC^{2} \\BC^{2}=12^{2} +16^{2} \\BC^{2} =144+256\\BC=\sqrt{400} \\BC=20[/tex]
sinB=cateta opusa\ipotenuza
=AC\BC
=16\20 (simplificam prin 4)
=4\5
sinC=cateta opusa\ipotenuza
=AB\BC
=12\20 (simplificam prin 4)
=3\5
cosB=cateta alaturata\ipotenuza
=AB\BC
=12\20 (simplificam prin 4)
=3\5
cosC=cateta alaturata\ipotenuza
=AC\BC
=16\20 (simplificam prin 4)
=4\5
tgB=cateta opusa\cateta alaturata
=AC\AB
=16\12 (simplificam prin 4)
=4\3
tgC=cateta opusa\cateta alaturata
=AB\AC
=12\16 (simplificam prin 4)
=3\4
ctgB=cateta alaturata\cateta opusa
=AB\AC
=12\16 (simplificam prin 4)
=3\4
ctgC=cateta alaturata\cateta opusa
=AC\AB
=16\12 (simplificam prin 4)
=4\3
b) ΔABC-dr [tex]T.P.\\==>[/tex]
[tex]AC^{2} =BC^{2} -AB^{2} \\AC^2=900-324\\AC=\sqrt{576}\\ AC=24[/tex]
sinB=AC\BC
=24\30 (simplificare prin 6)
=4\5
sinC=AB\BC
=18\30 (prin 6)
=3\5
cosB=AB\BC
=18\30 (prin 6)
=3\5
cosC=AC\BC
=24\30 (simplificare prin 6)
=4\5
tgB=AC\AB
=24\18 (prin 6)
=4\3
tgC=AB\AC
=18\24 (prin 6)
=3\4
ctgB =AB\AC
=18\24 (prin 6)
=3\4
ctgC=AC\AB
=24\18 (prin 6)
=4\3
c)......... [tex]T.P.\\==>[/tex]
[tex]AB^2=BC^2-AC^2\\AB^2=1225-441\\AB=\sqrt{784}\\ AB=28[/tex]
sinB=AC\BC=21\35
sinC=AB\BC=28\35
cosB=AB\BC=28\35
cosC=AC\BC=21\35
tgB=AC\AB=21\28 (prin 7)=3\4
tgC=AB\AC=28\21 (prin 7)=4\3
ctgB=AB\AC=28\21 (prin 7)=4\3
ctgC=AC\AB=21\28 (prin 7)=3\4
d)...[tex]T.P.\\==>[/tex]
[tex]BC^2=AB^2+AC^2\\BC^2=576+1024\\BC=\sqrt{1600}\\BC=40[/tex]
sinB=AC\BC=32\40 (prin 8)=4\5
sinC=AB\BC=24\40 (prin 8)=3\5
cosB=AB\BC=24\40 (prin 8)=3\5
cosC=AC\BC=32\40 (prin 8)=4\5
tgB=AC\AB=32\24 (prin 8)=4\3
tgC=AB\AC=24\32 (prin 8)=3\4
ctgB=AB\AC=24\32 (prin 8)=3\4
ctgC=AC\AB=32\24 (prin 8)=4\3
e) [tex]T.P.\\==>[/tex]
[tex]AB^2=BC^2-AC^2\\AB^2=2025-729\\AB=\sqrt{1296}\\AB=36[/tex]
sinB=AC\BC=27\45 (prin 9)=3\5
sinC=AB\BC=36\45 (prin 9)=4\5
cosB=AB\BC=36\45 (prin 9)=4\5
cosC=AC\BC=27\45 (prin 9)=3\5
tgB=AC\AB=27\36 (prin 9)=3\4
tgC=AB\AC=36\27 (prin 9)=4\3
ctgB=AB\AC=36\27 (prin 9)=4\3
ctgC=AC\AB=27\36 (prin 9)=3\4
f) ..............[tex]T.P.\\==>[/tex]
[tex]AC^2=BC^2-AB^2\\AC^2=2500-900\\AC=\sqrt{1600}\\AC=40[/tex]
sinB=AC\BC=40\50 (prin 10)= 4\5
sinC=AB\BC=30\50 (prin 10)=3\5
cosB=AB\BC=30\50 (prin 10)=3\5
cosC=AC\BC=40\50 (prin 10)= 4\5
tgB=AC\AB=40\30 (prin 10)=4\3
tgC=AB\AC=30\40 (prin 10)=3\4
ctgB=AB\AC=30\40 (prin 10)=3\4
ctgC=AC\AB=40\30 (prin 10)=4\3
