Question

DAU COROANA ȘI 20 DE PUNCTE DOAR DACĂ FACEȚI CORECT! exercițiul 12

Answer 1

a) Sin C=8/17
sin C=AB/BC
8/17=16/BC =>BC =34 cm
In ∆ ABC dr =>TP
AB²+AC²=BC²
16²+AC²=34²
AC²=1156-256
AC=√900
AC=30 cm
P ABCD = AB+AC+BC =16+30+34=80cm

b)
Tg B=AC/AB
5/12=20/AB=>AB= 48 In ∆ABC dr =>TP
AB²+AC²=BC²
48²+20²=BC²
BC²= 2304+400
BC=√2704
BC=52 cn
P ABC=AB+AC+BC=48+20+52=120 cm

c)
cos C= AC/BC
3 /5=AC/15=>AC=9 cm
In ∆ ABC dr =>TP
AB² +AC² =BC²
AB² +9²=15²
AB² =225-81
AB=√144
AB=12 cm
P ABC =AB+AC+BC=12+9+15= 36 cm

d)
ctg B =AB/AC
3/4=18/AC=>AC=24
In ∆ ABC dr =>TP
AB² +AC² =BC²
18²+24²=BC²
BC²=576+324
BC=√900
BC=30 cm
P ABC = AB+AC+BC= 18+24+30=72 cm

Answer 2

B
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A______________C
a)sinC=AB/BC=8/17 =>BC=(17×16)/8=34 cm
t.Pitagora AC^2 = BC^2 - AB^2
AC^2 = (34-16)(34+16) = 18×50 =>AC=30 cm
P=16+34+30=80 cm

b)tgB=AC/AB=5/12 =>AB=(12×20)/5=48 cm
t.Pitagora BC^2 = AC^2 + AB^2
BC^2 = 400+2304 = 2704 =>BC=52
P=48+20+52=120 cm

c)cosC=AC/BC=3/5 =>AC=(3×15)/5=9 cm
t.Pitagora AB^2 = BC^2 - AC^2
AB^2 = (15-9)(15+9) = 6×24 =>AB=12 cm
P=15+9+12=36 cm

d)ctgB=AB/AC=3/4 =>AC=(4×18)/3=24 cm
t.Pitagora BC^2 = AB^2 + AC^2
BC^2 = 324+576 =900 => BC=30 cm
P=18+24+30=72 cm