Answer:
m<B = 28°
[tex] AB = 19.2 [/tex]
[tex] AC = 27.6 [/tex]
Step-by-step explanation:
Given:
m<A = 112°
m<C = 40°
AC = 14
Required:
Find, m<B, AB and BC.
SOLUTION:
✍️m<B = 180° - (112° + 40°) (sum of ∆)
m<B = 28°
✍️Using sine rule, find AB.
[tex] \frac{AB}{sin(C)} = \frac{AC}{sin(B)} [/tex]
Plug in the values into the equation.
[tex] \frac{AB}{sin(40)} = \frac{14}{sin(28)} [/tex]
Cross multiply
[tex] AB*sin(28) = 14*sin(40) [/tex]
Divide both sides by sin(28)
[tex] AB = \frac{14*sin(40)}{sin(28)} [/tex]
[tex] AB = 19.2 [/tex] (nearest tenth)
✍️Using sine rule, find BC.
[tex] \frac{BC}{sin(A)} = \frac{AC}{sin(B)} [/tex]
Plug in the values into the equation.
[tex] \frac{BC}{sin(112)} = \frac{14}{sin(28)} [/tex]
Cross multiply
[tex] AC*sin(28) = 14*sin(112) [/tex]
Divide both sides by sin(28)
[tex] AC = \frac{14*sin(112)}{sin(28)} [/tex]
[tex] AC = 27.6 [/tex] (nearest tenth)
