Answer:
A = 23°
b = 9.5
c = 14.7
Step-by-step explanation:
B = 32°
C = 125°
a = 7
✔️Find A:
A = 180° - (B + C) (sum of triangle)
A = 180° - (32° + 125°)
A = 23°
✔️Find b using Law of Sines:
[tex] \frac{sin(A)}{a} = \frac{sin(B)}{b} [/tex]
Plug in the values
[tex] \frac{sin(23)}{7} = \frac{sin(32)}{b} [/tex]
Cross multiply
[tex] sin(23)*b = sin(32)*7 [/tex]
Divide both sides by sin(23)
[tex] b = \frac{sin(32)*7}{sin(23)} [/tex]
b = 9.5 (nearest tenth)
✔️Find c using Law of Sines:
[tex] \frac{sin(A)}{a} = \frac{sin(C)}{c} [/tex]
Plug in the values
[tex] \frac{sin(23)}{7} = \frac{sin(125)}{c} [/tex]
Cross multiply
[tex] sin(23)*c = sin(125)*7 [/tex]
Divide both sides by sin(23)
[tex] c = \frac{sin(125)*7}{sin(23)} [/tex]
c = 14.7 (nearest tenth)
