Because $ \tan \theta = \frac512 \Rightarrow $ opposite = 5, adjacent = 12, hyp = 13. Then $ \sin \theta = \frac513 $, $ \cos \theta = \frac1213 $, so $ \sin 2\theta = 2 \sin\theta \cos\theta = 2 \cdot \frac513 \cdot \frac1213 = \frac120169 $. - go-checkin.com