A kitchen bench is in the shape of a segment of a circle. The segment is bounded by an arc of length 200 cm and a chord of length 160 cm. The radius of the circle is `r` cm and the chord subtends an angle `theta` at the centre `O` of the circle.
- Show that `160^2 = 2r^2 (1 - cos\ theta)`. (1 mark)
- Hence, or otherwise, show that `8 theta^2 + 25 cos\ theta - 25 = 0`. (2 marks)
- Taking `theta_1 = pi` as a first approximation to the value of `theta`, use one application of Newton’s method to find a second approximation to the value of `theta`. Give your answer correct to two decimal places. (2 marks)