All angles in this question are given in degrees.

A farmer owns land which lies between a wall and a hedge. The wall has a length of $50$ m and lies between points $O$ and $A.$ The hedge meets the wall at $O$ and the angle between the wall and the hedge is $28.$

The farmer plans to form a triangular field for her prizewinning goats by placing a fence with a fixed length of $25$ metres from point $A$ to the hedge. The fence meets the hedge at a point $B.$

The information is shown on the following diagram.

diagram not to scale

$($a$.$i$)$ Find the two possible size of O$$B$,$ giving your answers in degrees.

$[5]$

$($a$.$ii$)$ Hence, find the two possible areas of the triangular field.

$[3]$