Answer:
m∠A = 30°
m∠B = 80°
m∠C = 70°
Step-by-step explanation:
By applying cosine rule in the given triangle,
b² = a² + c² - 2ac[cos(∠B)]
From the given triangle,
a = 14 m
b = 28 m
c = 24 m
(28)² = (14)² + (24)² - 2(14)(24)cos(B)
784 = 196 + 576 - 672cos(∠B)
cos(∠B) = 0.1786
∠B = [tex]\text{cos}^{-1}(0.1786)[/tex]
∠B = 79.71°
∠B = 80°
By applying sine rule in the given triangle,
[tex]\frac{\text{sinA}}{a}= \frac{\text{sinB}}{b}= \frac{\text{sinC}}{c}[/tex]
[tex]\frac{\text{sinA}}{14}= \frac{\text{sin(79.71)}}{28}= \frac{\text{sinC}}{24}[/tex]
[tex]\frac{\text{sinA}}{14}= \frac{\text{sin(79.71)}}{28}[/tex]
[tex]\text{sinA}= \frac{\text{sin(79.71)}\times 14}{28}[/tex]
sinA = 0.491958
A = 29.47°
A ≈ 30°
By applying triangle sum theorem,
m∠A + m∠B + m∠C = 180°
30° + 80° + m∠C = 180°
m∠C = 70°
