G6.3 If $\tan \theta=\frac{-7}{24}, 90^{\circ}<\theta<180^{\circ}$ and $100 \cos \theta=r$, find $r$.
In the figure, $r^{2}=7^{2}+(-24)^{2}$ (Pythagoras' theorem)
$$
\begin{aligned}
r & =25 \\
r & =100 \cos \theta \\
& =100 \times \frac{-24}{25} \\
& =-96
\end{aligned}
$$