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})).
Explanation
(a)(i) < ASO = < AMO = 90° (radius to a tangent)
< SOM = 360° – (3 x 90°) (sum of angles of a rectangle)
= 90°.
(therefore) obtuse < SOT = 360° – (90° + 60° + 60°) = 150°.
(ii) Arc SRT = (frac{150°}{360°} times 2pi r)
= (frac{150}{360} times 2 times frac{22}{7} times 10 = frac{550}{21})
= (26.19cm)
(iii) (tan 60° = frac{TB}{10})
(TB = 10tan 60° = 17.32cm)
(b) Length of the string ASRTB = AS + arc SRT + TB
= 10cm + 26.19cm + 17.32cm
= 53.51cm (approxeq) 54cm.