Question

1) Fie ABC un triunghi dreptunghic cu m(A)=90:
a) calculati AB,AC si tg C, stiind ca BC=13 cm si sin B=12\13
b) aflati BC si sin B, daca AB=3 cm si AC=3√3 cm.
c) calculati AB,BC si CA, stiind ca sin C=3\5 si AB+BC=24m

Answer 1

a)sinB=AC/BC =>  AC/BC=12/13 => AC=12xBC/13=12cm
din Pitagora calc.AB^2=BC^2-AC^2  (^2==puterea a doua)
AB^2=169-144=25  =>  AB=5cm
tgC=AB/AC=5/12
b)din Pitagora BC^2=AB^2+AC^2=9+27=36  =>  BC=6cm si sinB=AC/BC=3V3/6=V3/2
c)sinC=AB/BC=3/5   =>  (AB+BC)/BC=(3+5)/5  =>  24/BC=8/5  => BC=24x5/8=15cm
=>  AB=24-15=9cm si din Pitagora AC^2=BC^2-AB^2=225-81=144 deci AC=12cm