sin ABC = 2/3=cateta opusa/ipotenuza=AC/BC
2/3=AC/BC
BC=3/2 AC
cos ABC= cateta alaturata/ipotenuza= AB/BC
teorema Pitagora: BC^2=AB^2+AC^2
inlocuim BC : (3/2 AC)^2=AB^2+AC^2
AB^2=(3/2 AC)^2-AC^2=9/4 AC^2 - AC^2= (9AC^2 - 4AC^2) /4=
=5/4 AC^2
Deci AB=(radical din 5/4) * AC^2 = AC * (radical din 5/4)
cos ABC= AB/BC inlocuim AB si BC
cos ABC= AC (radical din 5/4) : 3 AC/2 = AC (radical din 5/4) * 2/ 3AC=
= 2/3 (radical din 5/4)
(5/4 se afla in intregime sun radical de aia l-am pus in paranteze)
