Answer:
Option D is correct.
Step-by-step explanation:
Given,
In ΔABC, ∠A = 42° , ∠B = 56° & a = 7
We use law of sines,
which has following expression:
[tex]\frac{a}{sin\,A}=\frac{b}{sin\,B}\frac{c}{sin\,C}[/tex]
First we find value of ∠C
∠A + ∠B + ∠C = 180° (Angle Sum Property of Triangle)
42 + 56 + ∠C = 180
∠C = 180 - 98
∠C = 82°
Now using law of sines, we get
[tex]\frac{7}{sin\,42}=\frac{b}{sin\,56}[/tex]
[tex]\frac{7}{0.67}=\frac{b}{0.83}[/tex]
[tex]b=\frac{7}{0.67}\times0.83[/tex]
[tex]b=8.67[/tex]
[tex]\frac{7}{sin\,42}=\frac{c}{sin\,82}[/tex]
[tex]\frac{7}{0.67}=\frac{c}{0.99}[/tex]
[tex]c=\frac{7}{0.67}\times0.99[/tex]
[tex]c=10.36[/tex]
Therefore, Option D is correct.
