Question

lectia:lotiuni de trigonometrie in triunghiul freptunghic
EX:se considera dreptunghiul ABC,(<A)=90grade
a)daca AB=6cm si BC=10cm,calculati AC,sinC,cosC,tgB,ctgB
b)daca AB=5cm si AC=5radical3 cm,calculati BC,sinB,cosB,tgC,ctgC

Answer 1

a)ΔABC, mas<A=90   ⇒AC²=BC²-AB²= 100-36=64   ⇒AC=8
sin<C=  AB/BC=6/10=3/5
cos<C=AC/BC=8/10=4/5
tg<B=AC/AB=8/6=4/3
ctg<B=AB/AC=6/8=3/4

b)ΔABC, mas< A=90  ⇒BC²=AC²+AB²=  5²  +(5√3)²=25 + 75=100  ⇒BC=10
sin<B=AC/BC= 5√3/10  =√3/2   ⇒mas<B=60
cos<B=AB/BC=5/10=1/2
tg<C=AB/AC= 5/5√3= 1/√3=   √3/3 
ctg<C=AC/AB=5√3/5=√3

Answer 2

b)T.P. =>BC^2=AB^2+AC^2 =>BC^2=25+(5radical3)^2
BC=radical din 100=10cm
sinB=AC/BC=/10
cosB=AB/BC=5/10
tgC=sinC/cosC=0.5/(5 radical din 3/10)