A uniform lamina \(ABCDE\) consists of a square and an isosceles triangle. The square has sides of \(18 \text{cm}\) and \(BC = CD = 15 \text{cm}\) (see diagram).

###### There are **7** marks available for part (i) and **2** marks for part (ii).

###### In total, this question is worth **12.5%** of all available marks in the paper.

###### This is part of the set OCR A Level Problems.

\((\text{i})\) Taking \(x\)- and \(y\)-axes along \(AE\) and \(AB\) respectively, find the coordinates of the centre of mass of the lamina.

\((\text{ii})\) The lamina is freely suspended from \(B\). Calculate the acute angle that \(BD\) makes with the vertical.

**Input the angle in degrees, to three significant figures, as your answer.**

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