Chapter 7 - Section 7.3 - The Ambiguous Case - 7.3 Problem Set - Page 390: 20

$A = 90^\circ \hspace{10pt} C =60^\circ \hspace{10pt} c = 7.274 \,$ cm

$\sin{A} = \dfrac{a \sin{B}}{b} = \dfrac{8.4 \times \sin{30}}{4.2}$ $\sin{A} = 1$ $A = 90^\circ$ $C = 180-(A+B) = 60^\circ$ $c = \dfrac{b \sin{C}}{\sin{B}} = \dfrac{4.2 \times \sin{60} }{\sin{30}}$ $c = 7.274 \,$ cm