3.
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\caption{Figure 1}
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Figure 1 shows a decoration which is made by cutting the shape of a simple tree from a sheet of uniform card. The decoration consists of a triangle \(A B C\) and a rectangle \(P Q R S\). The points \(P\) and \(S\) lie on \(B C\) and \(M\) is the mid-point of both \(B C\) and \(P S\). The triangle \(A B C\) is isosceles with \(A B = A C , B C = 4 \mathrm {~cm} , A M = 6 \mathrm {~cm} , P S = 2 \mathrm {~cm}\) and \(P Q = 3 \mathrm {~cm}\).
- Find the distance of the centre of mass of the decoration from \(B C\).
The decoration is suspended from \(Q\) and hangs freely.
- Find, in degrees to one decimal place, the angle between \(P Q\) and the vertical.