Răspuns :
a)sinB = cateta opusa/ipotenuza = AC/BC
b)cosB = cateta alaturata/ipotenuza = √3/2 =>m(∡B)=60° =>F
c)tgB = cateta opusa/cateta alaturata = AC/AB =√3 =>AC=√3AB
t.inalt. =>AD²=BD·DC =>BD·DC=36
t.Pit. =>AB²+AC²=BC² sau AB²+3AB²=BC² =>BC²=4AB² =>BC=2AB
Stim ca BD+DC=BC =>BD+DC=2AB
t.cat.=>AB²=BD·BC sau AB²=BD·2AB =>AB=2BD
In Δdr.BDA cu t.Pit. avem BD²+AD²=AB² sau BD²+36=4BD² =>36=3BD² sau 12=BD² =>BD=2√3 cm
d)Cu t.Pit. avem AD²+DC²=AC² sau 36+DC²=100 =>DC²=64 =>DC=8 cm
e)Cu t.inalt. avem AD²=BD·DC =>36=BD·9 =>BD=4 cm
b)cosB = cateta alaturata/ipotenuza = √3/2 =>m(∡B)=60° =>F
c)tgB = cateta opusa/cateta alaturata = AC/AB =√3 =>AC=√3AB
t.inalt. =>AD²=BD·DC =>BD·DC=36
t.Pit. =>AB²+AC²=BC² sau AB²+3AB²=BC² =>BC²=4AB² =>BC=2AB
Stim ca BD+DC=BC =>BD+DC=2AB
t.cat.=>AB²=BD·BC sau AB²=BD·2AB =>AB=2BD
In Δdr.BDA cu t.Pit. avem BD²+AD²=AB² sau BD²+36=4BD² =>36=3BD² sau 12=BD² =>BD=2√3 cm
d)Cu t.Pit. avem AD²+DC²=AC² sau 36+DC²=100 =>DC²=64 =>DC=8 cm
e)Cu t.inalt. avem AD²=BD·DC =>36=BD·9 =>BD=4 cm