Question

in triunghiul dreptunghic Abc , varful A=90°, B = 60°, cateta Ac=6√3. calculati perimetru si inaltimea AD si bisectoarea BE

Answer 1

C=30° =>cateta opusa acestui unghi este jumatate din ipotenuza.
=>AB=BC/2
cos30=cateta alaturata/ipotenuza =>√3/2=AC/BC =>BC=12 cm
t.Pit.AB²+AC²=BC² =>AB²=144-108 =>AB²=36 =>AB=6 cm
t.cat. =>AB²=BD·BC =>36=BD·12 =>BD=3 cm =>DC=9 cm
t.inalt. =>AD²=BD·DC =>AD²=3·9 =>AD=3√3 cm
∡ABE≡∡EBC (BE-bisectoare)
In Δdr.BAE avem m(∡BEA)=60°(180-90-30)
=>sin60=AB/BE =>√3/2=6/BE =>BE=4√3 cm