Question

VA ROG!!! AJUTATI-MA!
 Intr-un triunghi ABC se cunosc m(ung.B)=45°,AB=3√2 si BC=4.Aflati perimetrul triunghiului.

Answer 1

sinB=AC/BC
BC²=AB²+AC²
BC²=144+25
BC²=169
BC=13
sinB=12/13
sinC=AB/BC
sinC=5/13
cosB=AB/BC=5/13
tgC=AB/AC
tgC=5/12
ctgB=AB/AC
ctgB=5/12
sin²B+cos²B=(12/13)²+(5/13)²=(144+25)/169=169+169=1

Answer 2

ducem AD inaltimea triunghiului ABC
ABD triunghi dreptunghic
cos B=BD/AB
BD=ABcosB
BD=3√2*√2/2=3⇒DC=1
sinB=AD/AB⇒AD=AB sinB=3√2*√2/2=3
ΔADC triunghi dreptunghic se aplica t lui Pitagora
AC²=AD²+DC²
AC²=9+1⇒AC=√10
PABC=3√2+√10+4