Question

Triunghiul ABC are m(A)=90°, m(B)=60°, AB=8. Sa se calculeze perimetrul triunghiului ABC.

Answer 1

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

Answer 2

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:

$tg(B)=\frac{cat.op.}{cat.al.} \\\\tg60=\frac{AC}{AB}\\\\\frac{\sqrt3}{1}=\frac{AC}{8}=>AC=8\sqrt3$

ΔABC-dr:

$sinC=\frac{cat.op}{ip.} \\\\sin30=\frac{AB}{BC}\\\\\frac{1}{2} =\frac{8}{BC}=>BC=16$

$P_{ABC}=AB+AC+BC\\P_{ABC}=8+8\sqrt3+16\\P_{ABC}=24+8\sqrt3\\P_{ABC}=8(3+\sqrt3)$

(factorul comun e optional; il pui daca vrei)

Succes!