G6.1 The average of $p, q, r$ is 4. The average of $p, q, r, x$ is 5. Find $x$.
G6.2 A wheel of a truck travelling at $60 \mathrm{~km} / \mathrm{h}$ makes 4 revolutions per second.
If its diameter is $\frac{y}{6 \pi} \mathrm{m}$, find $y$.

G6.3 If $\sin (55-y)^{\circ}=\frac{d}{x}$, find $d$.
G6.4 In the figure, $B A \perp A C$ and $A N \perp B C$. If $A B=3, A C=d$, $A N=h$, find $h$.
Reference: 1986 FG6.4, 1987 FG10.1, 1988 FG9.2
$$
\begin{array}{l}
p+q+r=12 \\
p+q+r+x=20 \\
x=8 \\
60 \mathrm{~km} / \mathrm{h}=\frac{60000}{3600} \mathrm{~m} / \mathrm{s}=\frac{50}{3} \mathrm{~m} / \mathrm{s} \\
\frac{y}{6 \pi} \times \pi \times 4=\frac{50}{3} \\
\Rightarrow y=25 \\
\sin 30^{\circ}=\frac{d}{8}=\frac{1}{2} \\
\Rightarrow d=4
\end{array}
$$

Reference: 1992 FI5.3
$$
\begin{array}{l}
B C^{2}=3^{2}+4^{2} \text { (Pythagoras' theorem) } \\
\Rightarrow B C=5
\end{array}
$$

Area of $\triangle A B C=\frac{1}{2} \cdot 5 \times h=\frac{1}{2} \cdot 3 \times 4$
$$
\Rightarrow h=\frac{12}{5}
$$