Question

In triunghiul ABC  cu m(unghi B)=90 grade, avem BC=2√5CM. SI SIN c=$\frac{√5}{3}$
Calculati AC,AB,cosC, tg C, ctg C.
Nu inteleg deloc exercitiile astea :)

Answer 1

ΔABC, mas<B=90
BC=2√5

sin<C= √5/3
cos<C= 1/sin<C=  1/ √5/3= 3/√5=  3√5/5

cos<C= BC/AC= 2√5/AC

2√5/AC=3√5/5   =>AC= 5*2√5/3√5=  10/3

sin<C= √5/3
sin<C= AB/AC= AB/10/3

AB/10/3= √5/3  =>AB= 10/3 * √5/3=  10√5/3/3= 10√5/3 *1/3=  10√5/9

tg<C= AB/BC=  10√5/9/2√5= 10√5/9 * 2√5= 5/9

ctg<C= BC/AB= 2√5/10√5/9= 2√5 * 9/ 10√5=  9/5