Question

URGENT!!

ΔABC este dreptunghic in A.Daca sinB-sinC=1supra5 si BC=30cm, calcuati perimetrul triunghiului.

Answer 1

ΔABC
AB=c  BC=a=30   AC=b
sinB- sin C= $\frac{b}{a} - \frac{c}{a} = \frac{AC}{30}- \frac{AB}{30}= \frac{AC-AB}{30} \\ sin B-sin C= \frac{1}{5} \\ deci \frac{AC-AB}{30} = \frac{1}{5} \\ AC-AB=6 \\ AC=AB+6 \\ Din teorema lui Pitagora : AB^{2} + AC^{2} = BC^{2} \\AB^{2} + (6+AB)^{2} = 30^{2} \\ AB^{2} +36+12 AB+ AB^{2}=900 \\ 2AB^{2} +12 AB -900+36=0 \\ AB^{2} +6AB-864=0 \\ delta =1764 \\ x1=18 \\ x2=-24 \\ dar AB este latura deci \\ AB=18 \\ AC=AB+6 \\ AC=18+6=24 \\ P=AB +AC+BC=18+24+30=72$