Question

Calculati aria triunghiului abc daca
a)AB=12cm AC=8cm si masura unghiului BAC =30grade
b)AC=6√2cm BC=6cm si masura unghiuluiACB=45 grade
c)AB=8√3BC=5cmsi masura unghiuluiABC=60 grade

Answer 1

ΔABC oarecare
Fie BE_|_ AC, E ∈ [AC]

Avem ΔBEA, mas<E= 90°
mas<A= 30° => mas<ABE= 60° => BE= AB:2= 6cm

ArieΔ=$\frac{b*h}{2}$
AΔ= $\frac{BE*AC}{2}$= $\frac{6*8}{2}$= $24 cm^{2}$

b) ΔABC oarecare
Fie BE_|_AC, E∈ [AC]

ΔBEC, mas<E= 90°
mas<C= 45° => ΔBEC dreptunghic isoscel⇒ BE=CE= 6√2cm
AΔ= 6√2·6√2:2= 24:2= 12cm²

c) ΔABC oarecare
Fie AE_|_ BC, unde E∈[BC]

Avem ΔAEB, mas<E= 90°
mas<B= 60°=>mas<BAE= 30°=> BE= AB/2= 4√3cm
AE= hΔ
h²= (8√3)²- (4√3)²
h²= 192- 48
h= √144= 12cm

AΔ= $\frac{12*5}{2} = \frac{60}{2} = 30 cm^{2}$