Question

in triunghiul ABC se cunosc laturile AB=24cm,BC=18radical3cm si masura unghiului B=30grade. Aflati aria si perimetrul, distanta de la varful C la AB

Answer 1

ducem inaltimea AD pe BC
m∡B=30⇒AD=AB/2⇒AD=12
cos30=√3/2
cos∡ABD=BD/AB⇒BD/24=√3/2⇒BD=12√3
DC=BC-BD⇒DC=18√3-12√3=6√3
inΔADC(m∡D=90)⇒AC²=DC²+AD²
AC²=6√3²+12²⇒AC²=108+144⇒AC²=252⇒AC=√252=6√7
A=(AD·BC)/2⇒A=(12·18√3)/2⇒A=108√3cm²
P=AB+BC+AC⇒P=24+18√3+6√7⇒P=6(√7+3√3+4)
construim inaltimea CE pe AB
A=(CE·AB)/2
108√3=(CE·24)/2⇒CE=(2·108√3)/24⇒CE=9⇒d(C,AB)=9 cm