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Question id: 8. This question is similar to one that appeared in an IB Standard paper in 2010. The use of a calculator is allowed.

### Trigonometry

The diagram shows quadrilateral ABCD. Lengths are given in centimetres.

(a) Use the cosine rule to show that $$AC = \sqrt{130-126cosd}$$.

(b) Use the sine rule in triangle ABC to find another way of writing AC.

(c) (i) Hence find the value of $$d$$, assuming it is an obtuse angle, giving your answer to two the nearest degree.

(ii) Find AC.

(d) (i) Find $$b$$ to three significant figures.

(ii) Hence, or otherwise, find the area of triangle ACD.

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