Question

Fie triunghi dreptunghic ABC in A Daca BC=30 cm si sinB-sinC=unu supra 5 aflati perimetrul triunghiului

Answer 1

sin B-sin C=1/5
AC/BC-AB/BC=1/5
(AC-AB)/30=1/5
AC-AB=6 
notam AB=a  
AC=a+6
Teorema lui Pitagora
AB^2+AC^2=BC^2
a^2+(a+6)^2=30^2
a^2+a^2+12a+36=900
2a^2+12a-864=0
a^2+6a-432=0
(a+24)(a-18)=0
a=18 cm .....AB=18
AC = a+6=24 cm
P=18+24+30=72 cm