Step 1:
Apply cosine and sine rules
[tex]\begin{gathered} Sin\text{e rule} \\ \frac{a}{\sin A}\text{ = }\frac{b}{\sin B}\text{ = }\frac{c}{\sin C} \\ Co\sin e\text{ rule} \\ c^2=a^2+b^2-2ab\text{ }\times\text{ cosC} \end{gathered}[/tex]
Step 2;
Use the cosine rule to find side c
a = 12, b = 22 , m
[tex]\begin{gathered} c^2=12^2+22^2\text{ - 2}\times12\times22\text{ }\times\text{ cos95} \\ c^2\text{ = 144 + 484 - 528}\times(-0.087) \\ c^2\text{ = 673.936} \\ c\text{ = }\sqrt[\square]{673.936} \\ c\text{ = 25.96 } \\ \text{c = 26} \end{gathered}[/tex]
Step 3:
Find angle A and B using the sine rule.
[tex]\begin{gathered} \frac{a}{\sin A}\text{ = }\frac{c}{s\text{inC}} \\ \frac{12}{\sin A}\text{ = }\frac{26}{s\text{in95}} \\ \sin A\text{ = }\frac{12\text{ }\times\text{ sin95}}{26} \\ \sin A\text{ = }\frac{12\text{ }\times\text{ 0.99619}}{26} \\ \sin A\text{ = 0.4597821684} \\ A=sin^{-1}(0.4597821684) \\ A\text{ = 27.4} \\ A\text{ }\approx\text{ 27}.6\text{ } \end{gathered}[/tex]
Final part
Apply sum of angles in a triangle
A + B + C = 180
27.6 + B + 95 = 180
B = 180 - 95 - 27.6
B = 57.4
Final answer
c = 26 , A = 27.6 , B = 57.4 First option is the correct answer
