Question

Se considera triunghiul dreptunghic ABC,m( a.Daca AB=6 cm si BC=1 supra 2 calculati BC,AC,sin C,ctg B.
b.Daca AC=12 cm si tg C=1,25 calculati AB,BC,sinB,cosB.

Answer 1

AC^2=BC^2-AB^2=400-256=144 ⇒ AC=12 CM
SIN C=AB/BC=16/20=4/5
COS C=AC/BC=12/20=6/10=3/5
TG B=AC/AB=12/16
CTG B=AB/AC=16/12
SIN X= CATETA OPUSA/IPOTENUZA
COS X=CATETA ALATURATA/IPOTENUZA
TG X=CATETA OPUSA/CATETA ALATURATA
CTG X=CATETA ALATURATA/CATETA OPUSA=1/TG X
b)BC^2=AB^2+AC^2=36+36*3=36*4 rezulta BC=V36*4=6*2=12 , SINB=AC/BC=6V3/12,COS B=AB/BC=6/12=1/2,TG C=AB/AC=6/6V3=1/V3, CTGC=1/TGC=V3 
c)SIN C=AB/40=4/5 REZULTA CA AB=40*4/5=32 , AC^2=BC^2-AB^2=1600-1024=576 REZULTA AC=24, SIN B=AC/BC=24/40, COS B=AB/BC=32/40, TGC=AB/AC=32/24, CTGC=24/32