Chapter 7 - Applications of Trigonometric Functions - Section 7.3 The Law of Cosines - 7.3 Assess Your Understanding - Page 559: 36

$B \approx29.9^\circ$ $C\approx65.1^\circ$ $c \approx12.7$

1. Use the Law of Sines, we have $\frac{14}{sin85^\circ}=\frac{7}{sinB}=\frac{c}{sinC}$, thus $B=sin^{-1}(\frac{7sin85^\circ}{14})\approx29.9^\circ$ 2. Find the third angle $C\approx(180-85-29.9)=65.1^\circ$ 3. thus $c=\frac{14sin65.1^\circ}{sin85^\circ}\approx12.7$