Answer:
∠B = 74°
a ≈ 14.5 inches
c ≈ 11.4 inches
Step-by-step explanation:
The given parameters of triangle ΔABC are;
∠A = 62.2°, ∠C = 43.8° and side [tex]\overline{AB}[/tex] = b = 15.8 in
By sine rule, we have;
[tex]\dfrac{a}{sin(\angle A)} = \dfrac{b}{sin(\angle B)} = \dfrac{c}{sin(\angle C)}[/tex]
[tex]a = {sin(\angle A)} \times \dfrac{b}{sin(\angle B)}[/tex]
By angle sum property, we have;
∠B = 180° - (∠A + ∠C)
∴ ∠B = 180° - (62.2° + 43.8°) = 74°
∠B = 74°
[tex]\therefore {a} = {sin(62.2^{\circ})} \times \dfrac{15.8}{sin(74^{\circ})} \approx 14.5[/tex]
a ≈ 14.5 in.
[tex]c = {sin(\angle C)} \times \dfrac{b}{sin(\angle B)}[/tex]
[tex]\therefore {c} = {sin(43.8^{\circ})} \times \dfrac{15.8}{sin(74^{\circ})} \approx 11.4[/tex]
c ≈ 11.4 in.
