Question

i paralelogramul MNPQ avem MN_|_NQ ai m (MQN ) = 30 de grade NQ =12 radical din 3 cm calculati MN MQ MP va rog mult puteti da un raspuns exact

Answer 1

MNPQ-paralelogram
[QN] ; [MP] -diag
[QN]=[MP]= 12√3
[NQ]=12√3

ΔMNQ, mas < MNQ=90 ⇒ ΔMNQ-dreptunghic
mas < MQN=30

cos < MQN= QN/QM = 12√3/ QM
cos < MQN= cos <30 = √3/2

Din ambele relatii rezulta ca 12√3/ QM = √3/2

QM=  (12√3 * 2 )/ √3

QM= 12*2
QM=24

ΔMQN, mas <MQN=90

MN²= MQ²- QN²

MN²= 24² - ( 12√3)²

MN² = 576 - 432

MN²= 144 

MN=12