N*1)
a) BC² = AB² + AC²
= 6² + 5²
= 36 + 25
= 61
BC = [tex]\sqrt{61}[/tex]
= 7.81
b) cos ∠ABC = [tex]\frac{BA}{BC}[/tex]
= [tex]\frac{6}{7.81}[/tex]
= 39.80
c) sin ∠ABC = [tex]\frac{AC}{BC}[/tex]
= [tex]\frac{5}{7.81}[/tex]
= 0.64
N*2)
a) BC² = AB² + AC²
= 4² + 3²
= 16 + 9
= 25
BC = [tex]\sqrt{25}[/tex]
= 5
Donc ABC est un triangle rectangle car BC² = AB² + AC².
b) cos ∠BCA = BA / BC
= 3 / 5
= 53.13
sin ∠BCA = [tex]\frac{BA}{BC}[/tex]
= [tex]\frac{4}{5}[/tex]
= 0.8
