22. In $\triangle A B C, \angle A=85^{\circ}, c=10 \mathrm{~cm}$, and $b=15 \mathrm{~cm}$ A possible height of $\triangle A B C$ is a) $10.0 \mathrm{~cm}$ c) $13.8 \mathrm{~cm}$ b) $8.6 \mathrm{~cm}$ d) $12.5 \mathrm{~cm}$

Step 1 ：\(\sin A = \sin 85^\circ \approx 0.9962\)

Step 2 ：\(\sin B = \frac{b \sin A}{c} = \frac{15 \cdot 0.9962}{10} \approx 1.4943\)

Step 3 ：Since \(\sin B > 1\), there is no such triangle

Step 4 ：\(\sin C = \frac{c \sin A}{b} = \frac{10 \cdot 0.9962}{15} \approx 0.6642\)

Step 5 ：\(\angle C = \arcsin 0.6642 \approx 42^\circ\)

Step 6 ：\(\angle B = 180^\circ - \angle A - \angle C \approx 53^\circ\)

Step 7 ：\(h = b \sin A = 15 \cdot 0.9962 \approx \boxed{14.9}\)