Question

fie abc un triunghi ascutitunghic cu AB =4,BC=6, m(B)=60.calculati AC si sin (C)

Answer 1

Răspuns:

AC=2\/7 cm

Sin C=\/21/7

Explicație pas cu pas:

Rezolvarea este in imagine.

O zi senina!

Answer 2

$\it Th.\ Pitagora\ generalizat\breve a:\\ \\ AC^2=4^2+6^2-2\cdot4\cdot6 \cdot\ cos 60^o=16+36-2\cdot24\cdot\dfrac{1}{2}=52-24=28\\ \\ AC=\sqrt{28}=\sqrt{4\cdot7}=2\sqrt7\\ \\ \\ Th.\ sinusurilor:\\ \\ \dfrac{AB}{sinC}=\dfrac{AC}{sinB} \Rightarrow sinC=\dfrac{AB\cdot sinB}{AC}=\dfrac{4\cdot\dfrac{\sqrt3}{2}}{2\sqrt7}=\dfrac{4\sqrt3}{4\sqrt7}=\dfrac{^{\sqrt7)}\sqrt3}{\ \sqrt7}=\dfrac{\sqrt{21}}7{}$