Question

Se considera un triunghi ascutitunghic ABC cu AB=2,BC=5 si aria egala cu 4. Calculati cosB.

Answer 1

A(ABC)=AB x BC x sin(<B)/2
4=2 x 5 x sin(<B)/2
5sin(<B)=4==>sin(<B)=4/5;
dar sin(<B)^2+cos(<B)^2=1==> 16/25 +(cosB)^2=1==> (cosB)^2=1-16/25==>
(cosB)^2=9/25==>cosB=3/5