\(\frac{2\sin 30 + 5\tan 60}{\sin 60}\) \(\sin 30 = \frac{1}{2}; \tan 60 = \sqrt{3}; \sin 60 = \frac{\sqrt{3}}{2}\) \(\therefore \frac{2\sin 30 + 5\tan 60}{\sin 60} = \frac{2(\frac{1}{2}) + 5(\sqrt{3})}{\frac{\sqrt{3}}{2}}\)\) = \(\frac{1 + 5\sqrt{3}}{\frac{\sqrt{3}}{2}}\) = \(\frac{2(1 + 5\sqrt{3})}{\sqrt{3}}\) = \(\frac{2 + 10\sqrt{3}}{\sqrt{3}}\) Rationalizing, we get = \(\frac{2\sqrt{3} + 30}{3}\) = \(\frac{2}{3} \sqrt{3} + 10\)