Finding angle from geometry

A question is this type if and only if it requires using trigonometry or geometric relationships (sine rule, cosine rule, Pythagoras) to find an angle that is then used in arc/sector formulas.

1 questions · Standard +0.3

1.05b Sine and cosine rules: including ambiguous case1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta
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AQA C2 2013 June Q2
8 marks Standard +0.3
2 The diagram shows a sector \(O A B\) of a circle with centre \(O\). \includegraphics[max width=\textwidth, alt={}, center]{f4f090a1-7e36-4993-a49e-b6e7e8589057-2_341_371_968_815} The radius of the circle is 20 cm and the angle \(A O B = 0.8\) radians.
  1. Find the length of the arc \(A B\).
  2. Find the area of the sector \(O A B\).
  3. A line from \(B\) meets the radius \(O A\) at the point \(D\), as shown in the diagram below. \includegraphics[max width=\textwidth, alt={}, center]{f4f090a1-7e36-4993-a49e-b6e7e8589057-2_344_371_1747_815} The length of \(B D\) is 15 cm . Find the size of the obtuse angle \(O D B\), in radians, giving your answer to three significant figures.