Răspuns:
Explicație pas cu pas:
sin B = AC/BC
BC = AC/sin B = 4 /(1/2) = 8 cm
BC^2 = AC^2 + AB^2
AB^2 = BC^2 - AC^2 = 64 - 16 = 48
AB = √48 = 4√3 cm
A = AC*AB/2 = 4*4√3/2 = 8√3 cm^2
Salut!
ΔABC:
AC=4
m(∡A)=90°
m(∡B)=30°
⇒m(∡C)=180°-m(∡A)-m(∡B)
m(∡C)=180°-90°-30°
m(∡C)=60°
[tex]A_{ABC}=A_{tr.dreptunghic}[/tex]
[tex]A_{ABC}=\frac{c_1*c_2}{2}[/tex]
[tex]c_1=AC=4\\c_2=AB=?[/tex]
ΔABC-dr:
[tex]tgC=\frac{cat.op.}{cat.al.} \\\\tg60=\frac{AB}{AC}\\\\\frac{\sqrt3}{1} =\frac{AB}{4} =>AB=4 \sqrt3[/tex]
[tex]A_{ABC}=A_{tr.dreptunghic}[/tex]
[tex]A_{ABC}=\frac{c_1*c_2}{2} \\\\A_{ABC}=\frac{AC*AB}{2} \\\\A_{ABC}=\frac{4*4\sqrt3}{2}\\\\A_{ABC}=\frac{16\sqrt3}{2}\\\\A_{ABC} =8\sqrt3cm^2[/tex]
Succes!
