a) State or imply area of segment is $\frac{1}{2}{r^2}\theta  - \frac{1}{2}{r^2}\sin \theta $ or $50\theta  - 50{\text{ }}\sin \theta $

Attempt to form equation from area of segment $ = \frac{1}{5}$ of area of circle, or equivalent

Confirm given result $\theta  = \frac{2}{5}\pi  + \sin \theta $

b) Use iterative formula correctly at least once

Obtain value for $\theta $ of $2.11$

Show sufficient iterations to justify value of $\theta $ or show sign change in interval $\left( {2.105,{\text{ }}2.115} \right)$

Use correct trigonometry to find an expression for the length of $AB$

e.g. $20\sin {\text{ }}1.055$ or $\sqrt {200 - 200\cos 2.11} $

Hence $17.4$

$\left[ {2.1 \to 2.1198 \to 2.1097 \to 2.1149 \to 2.1122} \right]$