Question

Triunghiul ABC dreptunghic in unghiul A are AB= 2 cm si sin C=3/4. Calculati:a)BC b)AC c)sin B d)ctg C e) inaltimea corespunzatoare ipotenuzei

Answer 1

a)sinC=3/4=AB/BC=>3/4=2/BC=>BC=8/3
b)AC²+AB²=BC²
AC²=BC²-AB²
AC²=64/9-4
AC²=(64-36)/4
AC²=28/4=>AC=2√7/2=>AC=√7
c)sinB=3√7/8
d)ctgC=√7/2
e)Fie,AD,inaltimea
Cu,t.cat.avem
AC²=CDxCB
7=CDx8/3=>CD=21/8
BD=8/3-21/8=>BD=1/24
Cu,t.inaltimii
AD²=CDxDB
AD²=21/8x1/24=>AD²=21/192=>AD=√21/8√3=√21x√3/24=3√7/24
=>AD=√7/8