# Thread: Determine the lengths of BM and DN to 2 decimals places

1. ## Determine the lengths of BM and DN to 2 decimals places

The answer is approximately 2.29
I attempted to use sine law in order to find DN and my answer was close
$\frac{sin70}{6}=\frac{sin20}{DN}$
$\frac{sin70}{6}=0.157$
$\frac{sin20}{0.157}=DN=2.18$

Is there another method of solving this problem?

2. I got the answer
$\frac{6(DN)=(6-DN)(6-DN)}{2}$
$(6-DN)(6-DN)=36-12DN-DN^2=DN^2-12DN+36$
$DN^2-12DN+36=6DN$
$DN^2-18DN+36=0$
then use the quadratic equation....