Question

Determinati masurile unghiurilor unui triungi ABC, STIIND CA AB =3 RAD 6 SI AC=3 RAD 2 CM

Answer 1

Fie AM ⊥BC=> AM-inaltime

BC=BM+MC

In ΔAMB , m(∡M)=90°=>AM²=AB²-BM² (1)

In ΔAMC , m(∡M)=90°=>AM²=AC²-MC² (2)

(1)-(2)=0=AB²-AC²-BC²=>BC²=(3√6)²-(3√2)²=54-18=36=>BC=√36= 6 cm

Reciproca teoremei lui Pitagora :AC²+BC²=AB²<=>(3√2)²+6²=(3√6)²<=>18+36=54<=>54=54 (A)=> ΔABC - dreptunghic , m(∡C)=90°

In ΔABC , m(∡C)=90°=> cos A=AC/AB=>cos A=3√2/3√6=√2/√6=√12/6=2√3/6=√3/2=>cos A=√3/2=>m(∡A)=30°

m(∡B)=180°-(90°+30°)=180°-120°=60°=>m(∡B)=60°