Question

Find all the missing elements:

Answer 1

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,

$\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC} \\ \frac{a}{sinA} = \frac{7}{sin60} = \frac{3}{sinC} \\ \frac{7}{sin60} = \frac{3}{sinC} \\ sinC = \frac{3}{7} \: sin60 = 0.3711537445 \\ \\ C = 21.78$

cosine rule says,

${a}^{2} = {b}^{2} + {c}^{2} + 2bc \: cos(B) \\ {a}^{2} = {7}^{2} + {3}^{2} + 2(7)(3) \: cos(60) \\ {a}^{2} = 49 + 9 + \:21 = 79 \\ a = 8.88$