Răspuns:
Explicație pas cu pas:
AD = 20 cm ; tgB = 4/3
tgB = CE/BE = 20/BE = 4/3 =>
BE = 20·3/4 = 15 cm =>
AB = AE + BE = 20 cm + 15 cm = 35 cm
ΔBCE = dreptunghic =>
BC² = CE²+BE² = 20²+15² = 400+225 = 625
BC = √625 = 25 cm
P trapez = AB + BC + CD + AD =
= 35 cm+ 25 cm+ 20 cm+ 20 cm = 100 cm
P trapez = 100 cm
sin ACB = ?
AB/sinACB = AC/sinB
sinB = CE/BC = 20/25 = 4/5
AC² = AD²+CD² = 20²+20² = 400+400 = 800
AC = √800 = 20√2 cm =>
sinACB = AB·sinB / AC = (35·4/5) /20√2 = 28/20√2 = 7/5√2 =
= 7√2/10
