The cosine rule states that:
[tex]a^2=b^2+c^2-2bc\cos A[/tex]
For the given triangle:
a= BC
b=AC=12
c=AB=9
∠A=87º
Replace the known measures on the formula:
[tex]BC^2=12^2+9^2-2(9\cdot12\cdot\cos 87)[/tex]
Solve the exponents and the multiplication on the last term:
[tex]\begin{gathered} BC^2=144+81-216\cos 87 \\ BC^2=213.695 \end{gathered}[/tex]
-Apply the square root to both sides of the expression:
[tex]\begin{gathered} \sqrt[]{BC^2}=\sqrt[]{213.695} \\ BC=14.618 \\ BC\approx14.62 \end{gathered}[/tex]
The length of side BC is 14.62units
