Răspuns:
Explicație pas cu pas:
<C = 90° - 60° = 30°
sin C = AB/BC
BC = AB/(sin C) = 8/(1/2) = 16 cm
sin B = AC/BC
AC = BC*sin B = 16*√3/2 = 8√3 cm
P = BC + AB + AC = 16 + 8 + 8√3 = 24 + 8√3 cm
Salut!
ΔABC:
AB=8
m(∡A)=90°
m(∡B)=60°
⇒m(∡C)=180°-m(∡A)-m(∡B)
m(∡C)=180°-90°-60°
m(∡C)=30°
ΔABC-dr:
[tex]tg(B)=\frac{cat.op.}{cat.al.} \\\\tg60=\frac{AC}{AB}\\\\\frac{\sqrt3}{1}=\frac{AC}{8}=>AC=8\sqrt3[/tex]
ΔABC-dr:
[tex]sinC=\frac{cat.op}{ip.} \\\\sin30=\frac{AB}{BC}\\\\\frac{1}{2} =\frac{8}{BC}=>BC=16[/tex]
[tex]P_{ABC}=AB+AC+BC\\P_{ABC}=8+8\sqrt3+16\\P_{ABC}=24+8\sqrt3\\P_{ABC}=8(3+\sqrt3)[/tex]
(factorul comun e optional; il pui daca vrei)
Succes!