Question

Triunghiul ABC are m(A)=90°, m(B)=30°, AC=4. sa se calculeze aria triunghiului ABC.

Answer 1

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

Answer 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°

$A_{ABC}=A_{tr.dreptunghic}$

$A_{ABC}=\frac{c_1*c_2}{2}$

$c_1=AC=4\\c_2=AB=?$

ΔABC-dr:

$tgC=\frac{cat.op.}{cat.al.} \\\\tg60=\frac{AB}{AC}\\\\\frac{\sqrt3}{1} =\frac{AB}{4} =>AB=4 \sqrt3$

$A_{ABC}=A_{tr.dreptunghic}$

$A_{ABC}=\frac{c_1*c_2}{2} \\\\A_{ABC}=\frac{AC*AB}{2} \\\\A_{ABC}=\frac{4*4\sqrt3}{2}\\\\A_{ABC}=\frac{16\sqrt3}{2}\\\\A_{ABC} =8\sqrt3cm^2$

Succes!