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suma unghiurilor=180
105+45+C=180, C=30
teorema sinusului
AB/sin30=AC/sin45
AB=ACsin30/sin45=(20x1/2)/√2/2=10√2
ducem AD inaltimea AD perpendicular pe BC
ABD triunghi dreptunghic
cos 45=BD/AB, BD=ABcos45=10√2x√2/2=10
ADC triunghi dreptunghic
cos30-DC/AC, DC=AC cos 30=20x√3/2=10√3
BC=BD+DC=10+10√3
P=AB+BC+AC=10√2+30+10√3

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Davidpiscot Davidpiscot · Answer 2 · 2016-03-23T16:41:10+02:00

m A=105
m B=45
AC=20
m C=?
P=?
A+B+C=180 grade
C=180-A-B
C=180-105-45=30
C=30 de grade
Ducem perpendiculara din A ppe BC,AM⊥BC=>ΔAMC si ΔAMB sunt dreptunghice
In ΔAMC
sin C=AM/BC
1/2=AM/20 =>AM=10 cm
Aplicam in ΔAMC teorema lui Pitagora:
MC²=AC²-AD²
MC²=400-100=300
MC=10√3 cm
In ΔAMB aplicam sin de B
√2/2=AM/AB <=>√2/ 2=10/AB=>AB=10√2 cm
Aplicam sa aflam si MB
MB²=AB²-MB²
MB²=200-100=100
MB=10
BC=MB+MC
BC=10+10√3
P=AB+AC+BC
P=10√2+20+10+10√3=30+10√2+10√3
P=10(3+√2+√3) cm