Question

In triunghiul ABC , m ( < A ) = 90* , m ( < C ) = 60* si AB = 6 cm . Aflati lungimea segmentului AC .  ( urgent ) .

Answer 1

ΔABC, mas<A=90 
sin<C=60  =√3/2
sin<C=AB/BC= 6/BC

6/BC=√3/2

BC=6*2/√3=  6*2√3/3=  2*2√3=4√3

AC²=BC²-AB²=(4√3)²-6²= 48-36 =12  ⇒AC=2√3

Answer 2

AC= x
m(B)= 30 grade ⇒BC= 2x
in triunghiul ABC aplicam teorema lui Pitagora
BC²=AC²+AB²
(2x)²=x²+6²
4x²-x²=6²
3x²=36
x²=12 ⇒ x=√12=2√3  ⇒   AC= 2√3