Question

Un trapez dreptunghic ABCD , cu AB||CD , AB > CD , M(<A) = 90 grade , are diagonala AC perpendicularar pe latura BC. Daca m(<ABC) = 60 grade si BC = 12 cm , calculati lungimile bazelor trapezului

Answer 1

in triunghiul ABC m(BAC)=90-60=30 grade
sin 30 = 1/2 =CB/AC =12/AB
AB=12x2=24
AC=√(AB²-CB²)=√(24²-12²)=√(576-144)=√432=12√3 cm
m(BCD)=180-60=120 grade
AC_I_CB
m(DCA)=120-90=30 geade
in triunghiul ADC  cos 30=2/3=DC/AC=DC/12√3
DC=2/3 x 12√3=8√3 cm