Question

Intr-un triunghi dreptunghic ABC,m(∡A)=90°,AD⊥BC,D∈(BC),se da:
a)BC=25 cm si CD=16 cm.Calculati BD,AB si AC.

Answer 1

Aflam BD
Stim ca BC=BD+DC
BD=BC-CD
BD=25-16=9=>BD=9 cm
Aflam AB:
Aplicam teorema catetei pentru cateta AB
AB²=BD*BC
AB²=9*25
AB²= 225=>√AB=√225 cm =>AB=15 cm
Aflam AC cu teorema lui Pitagora :
AC²=BC²-AB²
AC²= 625-225=400=>AC²=400=>√AC=√400=20cm
Deci, AC=20cm