1. **State the problem:** We have triangle $\triangle TUV$ with side $t = 70$ inches opposite angle $T = 99^\circ$ and angle $U = 53^\circ$. We need to find the length of side $u$ opposite angle $U$. 2. **Find the missing angle:** The sum of angles in a triangle is $180^\circ$. $$ m\angle V = 180^\circ - m\angle T - m\angle U = 180^\circ - 99^\circ - 53^\circ = 28^\circ $$ 3. **Use the Law of Sines:** The Law of Sines states: $$ \frac{t}{\sin T} = \frac{u}{\sin U} $$ We want to find $u$, so rearrange: $$ u = \frac{t \sin U}{\sin T} $$ 4. **Substitute known values:** $$ u = \frac{70 \times \sin 53^\circ}{\sin 99^\circ} $$ 5. **Calculate sines:** $$\sin 53^\circ \approx 0.7986, \quad \sin 99^\circ \approx 0.9877 $$ 6. **Calculate $u$:** $$ u = \frac{70 \times 0.7986}{0.9877} = \frac{55.902}{0.9877} $$ 7. **Simplify fraction:** $$ u = \frac{\cancel{55.902}}{\cancel{0.9877}} \approx 56.6 $$ 8. **Round to nearest inch:** $$u \approx 57 \text{ inches} $$ **Final answer:** The length of side $u$ is approximately 57 inches.