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1 Pure Mathematics

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Question 72

A plan for an observation deck is shown below. The design consists of a major sector ABCOA ABCOA\,ABCOA of a circle with centre OOO, joined to a triangular viewing platform AODAODAOD. It is given that:

  • The radius of the circle OA=OC=10 mOA = OC = 10\text{ m}OA=OC=10 m
  • The platform edge AD=22 mAD = 22\text{ m}AD=22 m
  • The angle ∠ODA=0.40 radians\angle ODA = 0.40\text{ radians}∠ODA=0.40 radians
  • ∠AOD \angle AOD\,∠AOD is an obtuse angle
  • OCD OCD\,OCD is a straight line

Find:

Plan of the observation deck showing major sector ABCOA and triangular platform AOD, with O, C and D collinear.

a.

the size of angle AODAODAOD, in radians, to 3 decimal places,

[3]
b.

the length of arc ABCABCABC, in metres, to one decimal place,

[2]
c.

the total area of the deck, in m2\text{m}^2m2, to one decimal place.

[3]

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