Question

Trapezul drept. ABCD are AB\\CD,AB>CD,AC_|_BC, m(B)=60°,AD=18 cm si m(A)=m(D)=90°.Calculati: a)[BC], [AB], [DC] =?; b) lungimea diag AC; c) perimetrul ∆MDC, daca AD inters BC={M}. Va rog frumos, am nevoie de rezolvarea acestei probleme

Answer 1

a) facem in ΔADC cu cos DAC=18\AC=1\2 deci AC=18*2=36.
ΔACB => sin60=√3\2=36/AB=>AB=24√3.
sin CAB=1/2=> BC=36/2=18 cm
ΔDAC => cos 30=cosDCA=√3/2=CD/36 deci CD=18√2.
c)Aflam masura unghiului DCB=30+90=120°
deci m(MCD)=180-120=60°
cum ΔMCD dreptunghic rezulta ca m(DMC)=30° iar de aici aflam ipotenuza MC=2•18√2= 36√2.
iar DM=MC√3/2=18√6 (am facut sinMCD)
deci P=MD+DC+MC=18√6+54√2. poti sa mai scoti in factor comun daca vrei.