0 \leq\frac{|h_1^{2} \sin(\frac{1}{h_1}) + h_2^{2}|}{\sqrt{h_1^{2} + h_2^{2}}}
\leq \frac{h_1^{2} |\sin(\frac{1}{h_1})| + h_2^{2}}{\sqrt{h_1^{2} + h_2^{2}}} \leq \frac{h_1^{2} + h_2^{2}}{\sqrt{h_1^{2} + h_2^{2}}}=\sqrt{h_1^{2} + h_2^{2}}.