Answer/Step-by-step explanation:
3.a. length of AC.
Hypotenuse = AC
Opposite side to 60° = 7
Therefore, [tex] sin(60) = \frac{7}{AC} [/tex]
[tex] AC*sin(60) = \frac{7}{AC}*AC [/tex]
[tex] AC*sin(60) = 7 [/tex]
[tex] AC = \frac{7}{sin(60)} [/tex]
[tex] AC = 8.1 [/tex] (to nearest tenth)
b. Length of BC
Hypotenuse = BC
Opposite side to 50° = 7
Therefore, [tex] sin(50) = \frac{7}{BC} [/tex]
[tex] BC*sin(50) = \frac{7}{BC}*AC [/tex]
[tex] BC*sin(50) = 7 [/tex]
[tex] BC = \frac{7}{sin(50)} [/tex]
[tex] BC = 9.1 [/tex] (to nearest tenth)
c. Length of AB
Use the law of sines to find AB
[tex] \frac{BC}{sin(A)} = \frac{AB}{sin(C}} [/tex]
m<C = 180 - (60 + 50) (sum of angles in a triangle) = 70°
m<A = 60°
BC = 9.1
AB = ?
[tex] \frac{9.1}{sin(60)} = \frac{AB}{sin(70)} [/tex]
Cross multiply
[tex] 9.1*sin(70) = AB*sin(60) [/tex]
Divide both sides by sin(60)
[tex]\frac{9.1*sin(70)}{sin(60)} = \frac{AB*sin(60)}{sin(60)}[/tex]
[tex]\frac{9.1*sin(70)}{sin(60)} = AB[/tex]
[tex] 9.9 = AB [/tex] (nearest tenth)
[tex] AB = 9.9 [/tex]
