You have a triangle ABC with the following parameters:
a = ?
b = 12
c = 15
m∠A = 60
In order to calculate the value of side a, you use the Law of Cosines, which is given by the following formula:
[tex]a^2=b^2+c^2-2bc\cos (m\angle A)[/tex]Then, by replacing into the previous equation you have:
[tex]\begin{gathered} a^2=(12)^2+(15)^2-2(12)(15)\cos (60) \\ a^2=144+225-360(0.5) \\ a^2=189 \\ a=\sqrt{189}=13.74 \end{gathered}[/tex]Hence, the value of the length of side a is 13.74
