Răspuns:
Explicație pas cu pas:
a)
ΔCAB-∡A=90°
-∡B=30°
-∡ C=180-(30+90)= 60°
Teorema ∡de 30°→CB= 6x2=12cm
Teorema lui Pitagora →AB²=BC²-AC²→AB²=12²-6²→AB²=√108→AB=3√12
-
b)
∡F=45°
∡D=90°
∡E= 180-(90+45)=45°
∡F=∡E→ΔFDE= isoscel →FD=DE=7
FE²= 7²+7²=49+49=98
FE=√98= 7√2
-
c)
∡K=90°
LM- ipotenuza =8 si KM=4 →∡KLM= 30°
∡LMK= 180-(90+30)=60°
LK²=64- 16
LK²=√42=4√3
-
d)
∡G=90°
∡H=60°
∡J= 180-(90+60)=30°
teorema ∡ de 30°→JH= 3*2=6
JG²= 36-9=27
JG=√27=3√3 cm
-
e)
ΔSRT- isoscel →∡SRT= 180-(30+30)=120°
ST=12cm
RM⊥ST→RM- bisectoare ,mediana ,inaltime
ΔRTM-∡M=90°
-∡R=120:2=60°( RM- bisectoare)
-∡T=30°
TM=6 (RM-mediana)→RT=RS= 6*2=12cm
-
f)
ΔNPO= isoscel
MO⊥NP
MO= √16-12 ........prelungesti radicalul si la 12
MO=√4
MO= 2 cm
teorema ∡30°
∡MNO= 30°
NO/2= MO
∡NPO=∡PNO =30°
∡NOP= 180-(30+30)=120°
