Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.7 Apply Double-Angle and Half-Angle Formulas - 14.7 Exercises - Skill Practice - Page 959: 16

$\dfrac{2 \sqrt 5}{5}$

Need to divide the interval by $2$: Thus, we have $ \dfrac{\pi}{4} \lt \dfrac{a}{2} \lt \dfrac{\pi}{2}$ Since $\sin a$ is positive in the First quadrant. That is, $\sin \dfrac{a}{2} \gt 0$ Thus, $\sin \dfrac{a}{2}= \sqrt {\dfrac{1- \cos a}{2}}= \sqrt {\dfrac{1+(3/5)}{2}}$ $\sin \dfrac{a}{2} =\sqrt {\dfrac{4}{5}}=\dfrac{2 \sqrt 5}{5}$