Answer:
B. 21.64
Step-by-step explanation:
We have been given a triangle and we are asked to find the length of AC (b).
We will use law of cosines to find the length of side AC.
[tex]c^{2}=a^{2}+b^{2}-2ab \text{ cos }\theta[/tex]
Upon substituting our given values in the formula we will get,
[tex](AC)^{2}=15^{2}+12^{2}-2\times 15\times 12 \text{ cos}(106)[/tex]
[tex](AC)^{2}=225+144-360\text{ cos}(106)[/tex]
[tex](AC)^{2}=369-360(-0.275637355817)[/tex]
[tex](AC)^{2}=369+99.22944809412[/tex]
[tex](AC)^{2}=468.22944809412[/tex]
Upon taking square root of both sides of our equation we will be get,
[tex]AC=\sqrt{468.22944809412}[/tex]
[tex]AC=21.6386101238993629\approx 21.64[/tex]
Therefore, the length of b is 21.64 and option B is the correct choice.
