Question

ABCD e trapez, AB||CD
Unghiul A=120 de grade
Unghiul B=150 de grade
BC=12 cm
AB= 12 cm
AD=?
Linia mijlocie=?

Answer 1

ABCD e trapez, AB||CD Unghiul A=120 de grade
Unghiul B=150 de grade
BC=12 cm
AB= 12 cm
AD=?
Linia mijlocie=?
ducem AE si BF perpendiculare pe DC
m(<FBC)= 150⁰-90⁰=60⁰
m(<BCF)= 90⁰-60⁰=30⁰
m(<DAE)= 120⁰-90⁰=30⁰
m(<ADE)= 90⁰-30⁰=60⁰
in triunghiul BFC
sin 30⁰= BF/BC
1/2=BF/12
BF=6
sin 60⁰= FC/BC
√3/2=FC/12
FC=6√3

in triunghiul ADE
sin 60⁰= AE/AD
√3/2=6/AD
AD=4√3
sin 30⁰= DE/AD
1/2=DE/4√3
DE=2√3
DC=2√3+12+6√3=12+8√3
Linia mijlocie=(AB+DC)/2=(12+12+8√3)/2=12+4√3