Chapter 7 - Analytic Trigonometry - 7.6 Double-angle and Half-angle Formulas - 7.6 Assess Your Understanding - Page 497: 36

$\frac{1+\sqrt 5}{2}$

Step 1. Using the given figures, we have $a=-\sqrt {5-4}=-1, b=-\sqrt {1-\frac{1}{16}}=-\frac{\sqrt {15}}{4}$ Step 2. $h(\frac{\theta}{2})=tan(\frac{\theta}{2})=\frac{1-cos\theta}{sin\theta}=\frac{1-(-\frac{\sqrt 5}{5})}{\frac{2\sqrt 5}{5}}=\frac{1+\sqrt 5}{2}$