Answer:
C = 21.78 and a= 8.88
Step-by-step explanation:
Here, sides b=7 and c=3
Also, Angle B=60
Angle B is between side c and a
It can be solve by cosine rule and sin rule
sin rule says,
[tex] \frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC} \\ \frac{a}{sinA} = \frac{7}{sin60} = \frac{3}{sinC} \\ \frac{7}{sin60} = \frac{3}{sinC} \\ sinC = \frac{3}{7} \: sin60 = 0.3711537445 \\ \\ C = 21.78[/tex]
cosine rule says,
[tex] {a}^{2} = {b}^{2} + {c}^{2} + 2bc \: cos(B) \\ {a}^{2} = {7}^{2} + {3}^{2} + 2(7)(3) \: cos(60) \\ {a}^{2} = 49 + 9 + \:21 = 79 \\ a = 8.88[/tex]
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