Question

Fie ABC un triunghi dreptunghic cu m(A)=90.a)calculati AB,BC si sin C,stiind ca AC=6 cm si tgB=2.b)determinatiAB,BC si CA,stiind ca BC=12 cm si sin B=12supra13

 

Answer 1

a)tgB=2
tgB=AC/AB⇒AB=AC/tgB
AB=6/2=3
ΔABC-dreptunghic, m(A)=90⇒AB²+AC²=BC²⇒3²+6²=BC⇒BC=3√5
sinC=AB/BC=3/3√5⇒sinC=1/√5

b) sinB=AC/BC⇒AC=BC·sinB
AC=144/13
ΔABC-dreptunghic, m(A)=90⇒AB²+AC²=BC²⇒AB²=BC²-AC²
AB²=144-20736/169⇒AB²=(24336-20736)/169⇒AB²=3600/169⇒AB=60/13