Acute, Obtuse or Right?

 $a^2+b^2=c^2\ \ \ RIGHT\ TRIANGLE$  

 $a^2+b^2<c^2\ \ \ OBTUSE\ TRIANGLE$  

 $a^2+b^2>c^2\ \ \ ACUTE\ TRIANGLE$  

What is the longest side?     

 $2\sqrt{15}=7.74$  so it is the longest side

 $4^2=16$   $6^2=36$  

 $\left(2\sqrt{15}\right)^2=2^2\times\left(\sqrt{15}\right)^2=4\times15=60$  

 $52<60\ \ \ so\ it's\ OBTUSE$  

 $\left(\frac{\sqrt{3}}{5}\right)^2=\frac{\left(\sqrt{3}\right)^2}{5^2}=\frac{3}{25}$  

 $\left(\frac{\sqrt{6}}{5}\right)^2=\frac{\left(\sqrt{6}\right)^2}{5^2}=\frac{6}{25}$  

 $\left(\frac{3}{5}\right)^2=\frac{9}{25}$