1. a) v PL (-1-11 ; 0-6)
v PL (-12 ; -6)
b) PL^2 = 12^2 + 6^2
PL^2 = 144 + 36 = 180
PL = √180
PL = 6√5
2. v LI = (2+1 ; -6-0)
v LI = (3 ; -6)
LI^2 = 3^2 + 6^2
LI^2 = 9 + 36 = 45
LI = √45
LI = 3√5
v PI (2-11 ; -6-6)
v PI (-9 ; -12)
PI^2 = 9^2 + 12^2
PI^2 = 81 + 144 = 225
PI = √225
PI = 15
3. LI^2 + PL^2 = 45 + 180 = 225
225 = PI ^2
Donc le triangle PLI est rectangle
4. Sin (LPI) = IL / PI
Sin (LPI) = 3√5 / 15
Sin (LPI) = √5 / 5
arcsin ≈ 27°
5. Sin (PIL) = PL / PI
Sin (PIL) = 6√5 / 15
Sin (PIL) = 2√5 / 5
arcsin ≈ 63°
