b) en exprimant de 2 façons tan (BAC) ; montrer que BD = 10 cm
tan (BAC) = BD/AB
tan (BAC) = BC/AC
Donc BD/AB = BC/AC ⇔BD x AC = AB x BC ⇒ BD = AB x BC/AC
BD = 6 x 7.5/4.5 = 45/4.5 = 10 cm
c) en déduire que AD = 12.5 cm
AD² = AB² + BD² = 7.5² + 10² = 156.5 ⇒ AD = √156.5 = 12.5 cm
d) on applique la réciproque du théorème de Thalès
AN/AB = AC/AD
2.7/7.5 = 4.5/12.5
0.36 = 0.36 ⇒ (NC) // (BD)
e) NC/BD = 0.36 ⇒ NC = 0.36 x BD = 0.36 x 10 = 3.6 cm
f) DM/BD =DC/DA ⇔ DM x DA = BD x DC ⇒DM = BD x DC / DA
DM = 10 x 8/12.5 = 6.4 cm
g) NBMC est un rectangle
MN² = BN² + NC² = 4.8² + 3.6² = 23.04 + 12.96 = 36
MN = √36 = 6 cm
h) 100 x 17.28/17.28 = 100
i) MN = 100 x 6 = 600 cm soit MN = 6 m
