In the diagram, ASRTB represents a piece of string passing over a pulley of radius 10cm in a vertical plane. O is the centre of the pulley and AMB is a hori...

In the diagram, ASRTB represents a piece of string passing over a pulley of radius 10cm in a vertical plane. O is the centre of the pulley and AMB is a horizontal straight line touching the pulley at M. Angle SAB = 90° and angle TBA = 60°. 

(a) Calculate (i) the obtuse angle SOT ; (ii) arc SRT ; (iii) |BT| 

(b) Find, correct to the nearest cm, the length of the string. (Take \(\pi = \frac{22}{7}\)).