Question

13)MNP triunghi dreptunghic
m(<N)=90 grade
m(<M)=60 grade
MN=8 cm
___________
Perimetriul si Aria lui MNP?

14)ABC triunghi dreptunghic
m(<A)=90 grade
AD perpendicular BC
D€BC
AD=12 cm
BD=9 cm
__________
laturile triunghiului,sin B,cos B,tg C,ctg C?

Answer 1

13)m(<P)=180-90-60=30 de grade
NM este cateta opusa unghiului de 30 de grade=> MP=jumatate din ipotenuza=>MP=2*8=16cm.
Teorema lui Pitagora in triunghiul MNP=> MP²=MN²+NP²=>NP²=MP²-MN²=256-64=192
NP=√192=8√3
P=MN+NP+MP=8+16+8√3=8*(1+2+√3)cm
S=NP*NM/2=8*8√3/2=32√3cm²
14)Conform teoremei lui Pitagora in ΔABD=> AB²=AD²+BD² => AB²=144+81=225=> AB=√225=15 cm
Teorema catetei in ΔABC=> AB²=BC·BD=> BC=AB²/BD=225/9=25cm
Teorema lui Pitagora in ΔABC=> AC²=BC²-AB²=625-225=400=>AC=√400=> AC=20cm
sinB=AC/BC=20/25=4/5=0,8
cosB=AB/BC=15/25=3/5=0,6
tgC=AB/AC=15/20=3/4=0,75
ctgC=AC/AB=20/15=4/3=1,33