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

• February 1st 2009, 05:58 PM
iamanoobatmath
Determine the lengths of BM and DN to 2 decimals places
http://img116.imageshack.us/img116/8376/mathsch6.jpg
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?
• February 1st 2009, 07:06 PM
iamanoobatmath
$\frac{6(DN)=(6-DN)(6-DN)}{2}$
$(6-DN)(6-DN)=36-12DN-DN^2=DN^2-12DN+36$
$DN^2-12DN+36=6DN$
$DN^2-18DN+36=0$