Question

urgemttttttt   1)rezolvati triunghiul abcd an A   daca ac =8√3 si m(B)=60 grade,2)rezolvati triunghiul abc dreptunghic  an  A daca  sin de c =1 pe 2 si ac=3

Answer 1

1)m(A)+m(B)+m(C)=180, 90+60+m(C)=180=>m(C)=30
sinB=$\frac{AC}{BC} =>BC= \frac{AC}{sinB}= \frac{8 \sqrt{3} }{ \frac{ \sqrt{3} }{2} }=16$

cosB=$\frac{AB}{BC}=>AB=BC*cosB=16* \frac{1}{2}=8$


2)$sinC= \frac{1}{2}=>m(C)=30$
m(A)+m(B)+m(C)=180,  
90+30+m(B)=180=>m(B)=60
cosC=$\frac{AC}{BC}=>BC= \frac{AC}{cosC} = \frac{3}{ \frac{ \sqrt{3} }{2} } =2 \sqrt{3}$

tgC=$\frac{AB}{AC}=>AB=AC*tgC=3* \frac{ \sqrt{3} }{3} = \sqrt{3}$