Answer
$\frac{\sqrt 5+1}{2}$
Work Step by Step
1. $h(\frac{\theta}{2})=tan\frac{\theta}{2}=\frac{1-cos\theta}{sin\theta}$
2. Use the given figures, we have $sin\theta=\frac{2}{\sqrt 5}, cos\theta=-\frac{1}{\sqrt 5}$
3. $h(\frac{\theta}{2})=\frac{1+\frac{1}{\sqrt 5}}{\frac{2}{\sqrt 5}}=\frac{\sqrt 5+1}{2}$