8.
a)
ΔABC dreptunghic in A
∡B=30°
Teorema unghiului de 30° (latura care se opune unghiului de 30° este egala cu jumatate din ipotenuza
AC=BC:2
BC=2AC
BC=12 cm
Aplicam Pitagora (suma catetelor la patrat este egala cu ipotenuza la patrat)
BC²=AB²+AC²
144=AB²+36
AB²=108
AB=6√3 cm
∡C=180-30-90=60°
b)
∡F=45°
∡D=90°
∡E=180-90-45=45°
ΔFDE dreptunghic isoscel
FD=DE=7 cm
Pitagora:
FE²=FD²+DE²
FE²=49+49=98
FE=7√2 cm
c)
ΔLKM dreptunghic in K
KM=4 cm
LM=8 cm
LM=2KM⇒ ∡L=30°⇒ ∡M=60°
Aplicam Pitagora:
LM²=KM²+LK²
64=16+LK²
LK²=48
LK=4√3 cm
d)
ΔJGH dreptunghic in G
GH=3 cm
∡H=60° ⇒ ∡J=30°
HG=JG=H:2
JH=6 cm
Aplicam Pitagora:
JH²=JG²+GH²
36=9+JG²
JG²=27
JG=3√3 cm
e)
ΔRTS isoscel
RT=RS
TS=12 cm
∡S=∡T=30° ⇒ ∡R=180-30-30=120°
Ducem inaltimea RP⊥TS
RP=TR:2
TR=2RP
TP=6 cm
Aplicam Pitagora:
TR²=TP²+PR²
4RP²=36+RP²
3RP²=36
RP²=12
RP=2√3 cm⇒ TR=4√3 cm=RS
f)
ΔONP isoscel
NO=OP=4 cm
NP=4√3 cm
∡N=∡P
Ducem inaltimea OS⊥NP
SP=2√3 cm
Aplicam Pitagora:
OP²=OS²+SP²
16=OS²+12
OS²=4
OS=2 cm
OP=2OS⇒∡P=30°=∡N
Un alt exercitiu de geometrie gasesti aici: https://brainly.ro/tema/3859150
#SPJ5
