28. In $\triangle A B C$, $\angle C=3 \angle A, a=27$, and $c=48$. What is $b=$?
(A) 33;
(B) 35;
(C) 37,
(D) 39;
(E) the value of $\bar{\imath}$ is not unique.
28. By the Law of Sines, we have $\frac{27}{\sin A}=\frac{48}{\sin 3 A}$. Using the identity $\sin 3 A=3 \sin A-4 \sin ^{3} A$, we get
$$
\frac{48}{27}=\frac{16}{9}=\frac{\sin 3 A}{\sin A}=3-4 \sin ^{2} A .
$$
$=5 / 6$ (since $0<3 A<180^{\circ}$, $\cos A$ does not take a negative value). Using the Law of Sines again, we get
$$
\frac{b}{\sin \left(180^{\circ}-4 A\right)}=\frac{27}{\sin A}
$$

or $b=\frac{27 \sin 4 A}{\sin A}$.
From $\sin 4 A=2 \sin 2 A \cos 2 A=4 \sin A \cos A$
- $\left(\cos ^{2} A-\sin ^{2} A\right)$, we obtain
$$
b=27 \cdot 4 \cdot \frac{5}{6}\left(\frac{25-11}{36}\right)=35 .
$$
(B) is true.