Question

triunghiul ABC este dreptunghic in A. Daca sin B - sin C =1/5 si BC=30 cm, calculati perimetrul triunghiului

Answer 1

B
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A______________C

sinB=AC/BC
sinC=AB/BC
AC/BC - AB/BC = 1/5
(AC-AB)/BC = 1/5
(AC-AB)/30 = 1/5
5(AC-AB)=30
AC-AB=6 =>AC=AB+6
AC^2 + AB^2 = 900
(AB+6)^2 + AB^2 = 900
AB^2 + 12AB + 36 + AB^2 = 900 |:2
AB^2 + 6AB - 432 = 0
delta = 36+4•432=36+1728=1764 =>rad.delta=42
AB1=(-6-42)/2 nu e bun
AB2=(-6+42)/2=18
AC-18=6 =>AC=24
Perim.=18+24+30=72 cm